Thermodynamics, Infodynamics and Emergence

Emergence of novel processes, properties, structures, and systems is a poorly understood phenomenon. Emergence, information and energy are interrelated properties of nature: it takes free energy (energy that produces work, designed as F ) to acquire information, and it takes information to increment free energy. Useful information ( Φ ), is the one that increases free energy, and differs from information not producing free energy or producing entropy. Energy obeys all laws of thermodynamics, while information may not. When energy and information of systems interact, novel properties or levels of energy and information may emerge. Information can reveal itself in different forms (as entropy, order, complexity, physically encoded, mechanical, biological, structural, in neural or social networks, etc.). Information may increase free energy by reducing entropy in an open system, or by capturing free energy from the surroundings. The dynamics of information and energy has been studied mostly in physical-chemistry and engineering. Now we find it everywhere, including in computer sciences, genetics, biotechnology, experimental social sciences, and experimental law. In emergent systems new possibilities of increasing free energy and useful information appear. Emergent complexity is visible in the transitions from subatomic particles to atoms, from atoms to molecules, to cells, to organisms, to societies and ecosystems. A law for irreversible thermodynamics stating that Δ F ~ Δ Φ , is evidenced empirically in all these levels of complexity, confirming that increases in useful information and increments in free energy are coupled . As free energy helps access more information, and more information produces more free energy, evolution by natural selection accumulates ever more useful information, giving birth to life. In contrast, increases in entropy decreases free energy and might affect the amount of useful information available in the system. More noise or misleading information decreases useful information which decreases free energy. These relationships help us understand the evolution of life, societies, ecosystems, and autonomous artificial life. Quantifying concomitant changes in energy and information is needed to understand the relationship between them. The endeavor to achieve this has begun


Introduction
Information and energy are fundamental properties of nature, and emergence is a concept frequently used in complex system sciences. Here we refer to emergence as the phenomenon that makes novel unpredictable properties and features to appear in complex systems. We will use the dynamics of energy and information to understand emergence in simple and complex far-from-equilibrium systems. This research has the potential to revolutionize our understanding of the physical world, and it could lead to the development of new technologies that have the potential to improve our lives and that of our planet. Only by recognizing the multidimensional nature of information and energy will we be able to understand the emergence of complexity. The aim here is to formulate a conceptual framework that consiliently bridges our understanding of the dynamics of energy (thermodynamics), and that of information (infodynamics) to better Qeios,.0 · Article, July 2, 2023 Qeios ID: S90ADN.5 · https://doi.org/10.32388/S90ADN.5 2/23 thermodynamics can be summarized in its laws.

Laws of Thermodynamics
The zeroth law of thermodynamics says temperature is an empirical parameter in thermodynamic systems. It states the transitive relationship between the temperatures of multiple bodies in thermal equilibrium. The law says: If two systems are both in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This law implies that energy can flow spontaneously from high to low temperature systems but not the other way round.
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed. It can also be stated in the following form: The energy gained (or lost) by a system is equal to the energy lost (or gained) by its surroundings.
The second law of thermodynamics says that some things can't be undone after they are done. This indicates that entropy is a form of energy. It states that, in an isolated system, entropy can increase but cannot decrease. It can be stated as follows: Natural processes tend to go only one way, toward less usable energy and more entropy.
The third law of thermodynamics can be stated as: A system's entropy approaches a constant value as its temperature approaches absolute zero.

Dissipative systems
A proposed law or rule of irreversible thermodynamics for open far-from-equilibrium systems with a structure of minimum dissipation (Prigogine 1977) states that these systems maintain a stable state thanks to synergic processes that increase free energy concomitantly with gains in appropriate information. Lets call them synergistic systems. Quantitative empirical evidence from a variety of different systems (Jaffe 2023) suggest that synergistic systems occur at all levels of organizational complexity. In all known cases, free energy increases are coupled with increases in useful information.
No counter examples have been produced so far. That is, we do not know of any stable systems that increase its free energy while reducing its useful information. This proposed law might turn out to be a rule, if deduced from other laws and principles.

Free Energy
Energy might or might not be used to produce work. When it produces work we call it Free Energy, whereas Entropy is the energy that dissipates (as heat for example) without producing work. This work can be mechanical or chemical, but other kinds of work may also exist.

Helmholtz Free Energy
Our thermodynamic understanding of systems driven by kinetic energy is far more advanced than that of other forms of energy. As the relationship between information and emergence is rather diffuse, we might as well start with kinetic energy Where the abbreviations mean: F: Free Energy: the energy available in a system to do work E: Total Internal Energy of a system T: Temperature or the average kinetic energy of the system S: Entropy. The amount of total energy that cannot be used to produce work. measured in calories per kelvin per mole.
In information theory, entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes.
Free energy is a thermodynamic potential used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pressure. But energy exists also in systems not governed by pressure-volume work or chemical reactions. Thus we need to expand the concept of free energy. For example, in a steam locomotive, E relates to the total energy produced by the fire heating the water to produce vapor, and F refers to the actual pulling power the locomotive might exert using the vapor pressure. S relates to the energy lost in heat and other unusable forms during the process. Free energy also powers chemical reactions. In the example of the steam locomotive, the fire may be produced by burning coal. That requires the oxidation of coal or C + O 2 = CO 2 + Heat. The direction and extent of chemical change of this reaction can also be quantified using the free energy. In addition, the transfer of heat from the fire to the water molecules in order to produce vapor is also a process described by F.
The entropy concept applies to mechanical energy as a loss of energy due to production of heat produced by friction. It is because a macroscopic collective movement energy is partially distributed to chaotic, thermal movement of molecules. In thermodynamics transformation of order into disorder is what defines increase of entropy (Amiri et al 2010). Further expansions of the concept for free energy and entropy to other kinds of complex phenomena will be attempted here. The following concepts are relevant for this expansion.

Endergonic Processes
Processes that dissipate energy are called exothermic. Those that absorb energy are called endothermic. If what is dissipated is not heat but some other kind of energy, such as sound or light, we call the processes exergonic or endergonic. This last term is more general as it considers any kind of energy. Qeios, CC-BY 4.0 · Article, July 2, 2023 Endergonic reactions require a catalyst in order to proceed. This catalyst is a device that contains structural information (see below). These processes may reduce entropy as they absorb heat or other kinds of energy from the environment.
Here an example for Gibbs free energy is given. Equivalent plots can be drawn using other kinds of energy.

Potential Energy
Potential energy emerges when forces over a system are such that any trigger or change in border conditions can unleash a torrent of energy. We might refer to mechanical, electrical or chemical energy and examples include water dams, weights suspended in the air, chemical compounds that unleash energy, multidimensional systems that can store different kinds of energy to be used in special occasions such as armed forces prepared for war. All of these energies can be used to produce work.

Biological Energy
Biological organisms use different types of energy in their workings. The synergistic interactions between physiology and anatomy produces behaviors that can harness and/or produce energies of different kinds. These energies drive biochemical reactions and physiological processes and are expressions of free energy. For example the energy used for muscle contraction, the energy accumulated by a blood sucking mosquito, or the energy stored in a seed. These are mixes of chemical and mechanical energy studied by physiologists.

Social Energy
Biological aggregates of cells, organisms and/or ecosystems use different types of energy in its workings. The synergistic interactions between different components of a social system can harness and/or produce energies of different kinds.
These energies are used by the system to fuel the working of its components. They are free energy. An illustrative example Jaffe (2010) is given by the per capita energy consumption in societies of different sizes or complexity. As energy Qeios,.0 · Article, July 2, 2023 Qeios ID: S90ADN.5 · https://doi.org/10.32388/S90ADN.5 6/23 consumption per capita decreases, the free energy of the social system increases, as presented quantitatively for insect colonies and human cities in the figure.

Cognitive Energy
Conscious information or knowledge increases due to learning and research. These activities require work to produce the energy that increases information. Thus free energy can be identified in music and language. These increases in free energy are conspicuous when relating economic productivity of a country with the amount of scientific research activity.
Several examples are given in Jaffe (2023) Synergy Synergy refers to quantitative changes in energy due to non linear processes. This process might involve any of the types of energy listed above. Synergy occurs when information produces free energy.

Information
Information is a measure of a characteristic of energy and matter. In physics, information is used to describe the state of a system. For example, the position and momentum of a particle can be used to describe its state. In biology, information is used to describe the structure and function of biological systems. For example, the DNA sequence of a gene can be used to describe its structure, and the protein that is encoded by the gene can be used to describe its function. Thus, several types of information exist: Encrypted information such as that encoded in DNA or other biosemiotic devices, in music and in Language.
Transmissible information is normally encrypted onto a messenger. It is regarded as noise if the receptor has no clues as to how to decode it. Different types of information can be encrypted in different ways.
Negentropy or negative entropy. Often used as a proxy of information. But negative entropy is forbidden by the third law of thermodynamics, although negative changes in entropy are possible. That is always S > 0 but ΔS < 0 is possible. Best to avoid relating entropy to information in complex systems.
Chemical information contained in molecules that allow for specific interactions between different types of matter.
Electromagnetic information is transmitted through waves that interact at a distance Structural information or border conditions of machines and organisms and that of catalysts or molecules or structures that modulate chemical reactions or other processes Networks storing information. Neural networks in a brain, cell networks in an organ, computers, and social networks, for example. This information is not necessarily available to observes outside the system Spatial-Temporal information that allows synchronizing processes so as to produce work or synergy.

Others
No single tools exist to quantify all of these types of information. Strings of code can be analyzed with simple tools developed by physicists and information sciences, but they are of no help in quantifying structural information of complex catalytic molecules. A deeper understanding of the nature of information might help in this endeavor. Even as quantification of information is an unresolved challenge some attempts to do so include: Claude Shannon's 1948 paper "A Mathematical Theory of Communication". In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all distributions with a given mean and variance, the normal or Gaussian distribution is the one with the highest entropy. Kolmogorov A, (1965). Three Approaches to the Quantitative Definition of Information, Problems Inform. Transmission; is the root of what we know call Kolmogorov complexity. This type of complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Complexity and information related concepts. Complexity refers to the difficulty of understanding or describing a system, while information refers to the amount of knowledge that is needed to specify a system Schwartz, K. (2014) in "On the Edge of Chaos: Where Creativity Flourishes ¨ describes the concept of the "edge of chaos" as a metaphor for a state of dynamic balance between order and disorder. In this state, systems are able to adapt and change in response to new information and challenges, while still maintaining a basic level of structure and stability. This state is often associated with creativity, as it allows people to think outside the box and come up with new ideas. Deutsch, D. & Marletto, C (2015). "Constructor theory of information". The Constructor theory of Information is expressed solely in terms of which transformations of physical systems are possible and which are impossible -i.e. in constructor-theoretic terms. It includes conjectured, exact laws of physics expressing the regularities that allow Qeios, CC-BY 4.0 · Article, July 2, 2023 Qeios ID: S90ADN.5 · https://doi.org/10.32388/S90ADN.5 8/23 information to be physically instantiated. Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone.

Kolchinsky A., Wolpert D.H. (2021) "Work, Entropy Production, and Thermodynamics of Information under Protocol
Constraint" assumes that the thermodynamics of information in the presence of constraints can be decomposed into the information acquired in a measurement into "accessible" and "inaccessible" components. This decomposition allows considering the thermodynamic efficiency of different measurements of the same system, given a set of constraints. clear that the concept of information permeates all disciplines and that some more rigorous conceptualization of self organization and information is needed.
Haken, H., Portugali. J. (2016) presented Shannon's information that deals with the quantity of a message irrespective of its meaning, semantic and pragmatic forms of information that deal with the meaning conveyed by messages, and information adaptation that refers to the interplay between Shannon's information and semantic or pragmatic information. Gershenson, C., & Fernández, N. (2012) review in "Complexity and information: Measuring emergence, selforganization, and homeostasis at multiple scales" the relationship between these concepts. This comprehensive review on the subject shows that fundamental issues in the relationship between information and thermodynamics remain to be solved.
None of these approaches leads us to find a universal physical definition of Information. This justifies the present effort to build one such quantitative description. The description grows from the nature of information as a shadow of energy.

Complexity and Information
Complexity is more of a characteristic of information than an independent concept. Complexity refers to the degree of order or disorder in a system, while information refers to the amount of knowledge that is required to describe a system. In general, more complex systems require more information to describe. For example, a simple system like a rock can be described with a few simple properties, such as its size, shape, and color. A more complex system like a human being, on the other hand, requires much more information to describe, including its physical features, its personality, its memories, motivations and its thoughts.
The relationship between complexity and information has been nicely explored in biological evolution (Adami et al 2000) showing that because natural selection forces genomes to behave as a natural ''Maxwell Demon,'' within a fixed environment, genomic complexity is forced to increase.
Yet not all increase in complexity leads to an increase in useful information. Longer constitutions with more articles do not achieve better socioeconomic results of their countries than shorter ones. (Canova 2023). Nor do organisms that have longer DNA chains in their genome have always a higher complexity than others with less DNA. For example, the Australian lungfish has a genome with 43 billion base pairs, which is around 14 times larger than the human genome. Few would consider a lungfish more complex than a human. In general though, genome size is smaller for viruses than for bacteria, which in turn is smaller than that of vertebrates, etc.

Structural Information
The structure of an enzyme, the arrangements of components of a jet engine, or the architecture of a building carry information. The information required to build an enzyme, and the information that it transmits to the compounds it handles in chemical reactions is somehow reflected in its tridimensional structure. This information is directly related to the complexity of the structure. The more complex the structure the more information it carries and the more information is required to build it. Structural information is also related to the border conditions of a process (the restrictions the form of a cannon places on the interaction between the exploding powder and the cannonball). A chemical reaction is modulated by an enzyme that constraints the reaction, and thus imposes border conditions on it. However, not all information in a structure is useful in producing work.

Knowledge and Information
Information is the facts or details of a subject, whereas knowledge is awareness, understanding, or skills that involve this information. Information and knowledge refer to the same phenomenon. We might thus consider knowledge as another form of understanding information that can be coded in words or other means, or can be stored in neural or social networks.

Conclusions
We need to discern between useful and useless information analogous to our perception of energy which can (Free energy) or cannot (Entropy) be used to produce useful work. But different kinds of information have to be measured differently. Shannon information is useful for strings of data and Kolmogorov complexity can be estimated using length of verbal descriptions or computer algorithms. Structural information can be estimated by the number and diversity of the parts. Each system might have a peculiar way to measure information content. As we are interested in change of amount of information, the units are of less importance than the relative change in the estimate or proxy for information used.
Information is revealed in many different forms, such as complexity, knowledge, entropy, structures, order, dynamics, codes and networks, among others. Quantification of changes of each of these forms is possible, expanding previous notions of infodynamics (Salthe 2001). This allows us to study the relationship between infodynamics and thermodynamics in systems of different levels of complexity. In practical situations, complexity and its different forms is a first choice to estimate information, but many other forms exist (Jaffe 2023).

Infodynamics and Thermodynamics
Information may increase free energy as has been explained in physics by the story of Maxwell's demon (Nature 1867).
Real-life versions occur, and in all cases have their entropy-lowering effects duly balanced by increase of entropy elsewhere. Increases of free energy due to information are possible in open systems as entropy can exit the system and free energy can enter it. In these systems, quantitative empirical evidence shows that increases in information correlate with increased free energy in a multitude of different complex systems, from ant colonies to human society, and from music to legal norms (Jaffe 2023).
We might formalize these relationships generalizing Helmholtz equation, incorporating T in the conceptualization of S, as follows: Where Φ is useful information or the information that accounts for ΔF, I i are the different types of information and N is noise, useless information or information that produces entropy.
This last expression is consilient with Kolchinsky and Wolpert (2021) definition of "accessible" and "inaccessible" components of information, although they refer to different processes.
Using these abstractions we can write ΔF ~ ΔΦ as proposed by the fourth law (Jaffe 2023), based upon empirical evidence so far. The exact relation between F and Φ remains to be untangled but one link is the relation between S and N . In energetic terms S is related to the order or predictability of a system, and so is N . The problem here is that order and complexity are related, and these measures depend on the level of complexity addressed. This introduces distortions when comparing multiple levels or multiple dimensions of energy and information. This relationship means that in order to increase F there need to be an increase in Φ by increasing I or decreasing N. That is, not any type of information will do.
Information may be misleading, false and/or destructive provoking a reduction of F. We call this type of information N or noise. For now, the type of information, Φ or N, can only be assessed empirically by its effect on F. When increases of F are concomitant to increases Φ we may refer to a synergistic process. These limitations do not occur with energy, as relations between the different forms of energy are much better understood in physics than those of information. Thus I propose to use Φ as a proxy of useful information, order, complexity, and negative changes in entropy, until better concepts are developed.
The following examples may illustrate the issues.

Examples
Examples for far from equilibrium systems that suffer increase in free energy coupled with increase in information content.

Engine (heat)
Qeios, CC-BY 4.0 · Article, July 2, 2023 Qeios ID: S90ADN.5 · https://doi.org/10.32388/S90ADN.5 12/23 All engines produce heat when working. Its combustion process is exothermic. That is, only part of the energy contained in the fuel is converted to work. Another part is dissipated as heat. In physics, the first part is called Free Energy, the second part Entropy. During the process, F diminishes. The concept of information is needed to explain the thermodynamic behavior of this system regarding how the engine produces work.

Cannon (powder and ball)
A cannon ball placed upon a heap of fire powder will hardly move when the powder is burned. But if the fire powder is placed into a cannon with a cannon ball on top, the work produced by the flying cannonball after the explosive burning of the constrained powder is very large indeed. The cannon has more structural information modulating the power liberated by the burning powder (see also Constructor Theory by Deutsch & Marletto 2015) than the heap of powder. Also an engine has structural information that converts fuel to power. But not any border conditions or structure will do. The information relevant to obtain this free energy F we call useful information Φ.

Division of Labor
Qeios, CC-BY 4.0 · Article, July 2, 2023 Qeios ID: S90ADN.5 · https://doi.org/10.32388/S90ADN.5 13/23 Already Adam Smith recognized that division of labor confers greater economic capabilities of systems employing it. That is true for ant and for human societies alike. Evidence at the country level worldwide seems to suggest that more complex division of labor (more sophisticated technological networks) lead to more economic output (Haussman et al 2014). This increase in information production by country seems to be based mainly on increases in information in natural sciences (Jaffe et al 2013). Thus higher Φ produces more F.

Photosynthesis
A clever catalytic arrangement of molecules in an organelle in plant cells called chloroplast transforms light-energy, water and carbon dioxide into oxygen and energetic organic molecules (glucose). The process is endergonic in that it absorbs energy from the environment in the form of light photons and transforms it to chemical energy. It produces Free Energy F due to its highly complex structural information content Φ. (see Photosynthetic efficiency in Wikipedia) Qeios, CC-BY 4.0 · Article, July 2, 2023 Qeios ID: S90ADN.5 · https://doi.org/10.32388/S90ADN.5 14/23

Life and Sex
Erwing Schrödinger made the famous remark, "What an organism feeds upon is negative entropy". Referring to the fact that the organism succeeds in freeing itself from all the entropy it cannot help produce while alive. But it is also often stated that life feeds on negentropy, which in addition implies it consumes order that it harnesses for its benefit. I recommend avoiding the term negentropy and use that of Information instead. Information management is a fundamental requirement for evolution among living organisms (Jaffe 2000) and it allows incremental achievement of synergies that favor evolution. Specifically, sex achieves increases in genetic information that increases the useful information (Φ) for future generations. Life is a complex system that invented sex and cognition as a means to accelerate evolution to manage increments of Φ thanks to natural selection. That is, useful information (ΔΦ) produces increments in free energy (ΔF >0). As ΔF helps access more information triggering an evolutionary process aiming at ever more complexity and more F and Φ is possible (Jaffe 2018). This process is analogous to that described as autopoiesis by Maturana and Varela (1991). From the present perspective, natural selection favors useful information and discards the useless kind.

Socioeconomic and Politics
The more complex and multilevel de system, the more tangled up the information dynamics is. Free energy may be reduced by lack of adequate information or by the excess of misleading information such as excess religiosity (Jaffe 2005  presented in (Jaffe 2023). It takes free energy to acquire information, and it takes information to increment free energy.
This is the meaning of ΔF ~ ΔΦ. This definition is consilient with that given by the Constructor Theory (Deutsch & Marletto 2015) and the Constructal-theory (Bejan 1997). One way for information to increase free energy is by reducing entropy; but other more direct means are also possible in open systems. Information and energy are two different physical concepts: energy obeys all laws of thermodynamics, information may not. For example, information seems to increase in time concomitantly with entropy (Brooks 2001;Vopson & Lepadatu 2022). This might be due to the fact that entropy favors errors and mutations, which reflect in increases of information. Information can be structural or otherwise, and its action or connection to energy is studied mostly by applied sciences such as engineering, computer sciences, genetics, biotechnology, experimental social sciences, and experimental law.
These conclusions imply that ΔΦ is not necessarily related to ΔS e . That is, more or better information( Φ) may reduce the production of entropy of a process (increase efficiency) and so increase the free energy of the open system (F); but it might increase both, kinetic entropy (S e ) and free energy (F), but at different rates, by allowing the system to capture more energy from the environment. But F may only increase if Φ does, when no external flux of energy exists. However increases of the wrong kind of information might reduce F as the effect of fake news on social harmony and many other examples attest.

Multidimensional Systems and Emergence
A multidimensional system is a system in which more than one independent variable exists. Possible independent variables are for example time, color, odor, selection pressure, utility function, consilience, energy, information, etc. In multidimensional systems the output often depends on more than one input. Multidimensional systems are used to model complex phenomena, such as the weather, human behavior, societies and their dynamics, the stock market, and life.
However, most mathematical developments deal with up to 2 to 3 spatial dimensions. Some even include a fourth dimension: time. But very few include more. String theory includes up to eleven or more dimensions, but all these dimensions are mathematical constructs and have no known relation to reality.
Structural information emerges as a kind of multidimensional type of information as relevant information can be stored in different elements in a multidimensional system. A social structure, for example, must account for the different types of factors affecting its dynamic, some of them based upon very different dimensions. Thus emotions run on different natural laws than rational thinking, which in turn is dissociated with ecological constraints or with psychological experience. Each of these factors require a different dimension if we want to have an integral model of the system.
A single organism is dependent on features in multiple dimensions. The anatomical and physical constitution of the organism limits its possibilities to interact with space, whereas its metabolic structures limit its possibilities to extract order (to feed) from the environment, and its neurophysiological systems constrain its cognitive capabilities. All these features run on different dimensions that are required to describe an organism. Other dimensions such as chemical composition, physical features, energetic requirements, etc., are additional dimensions to be taken into account.
Emergence is a somewhat confusing term. It might refer to order or to complexity. In both cases it relates to information but in different thermodynamic conditions. A salt solution spontaneously settles to a crystal and thus, a spontaneous order emerges. But a seed spontaneously develops into a tree and a very much more complex order emerges. Both cases are referred to as self-organized. During crystallization, the chemical potential of the solution is lost, diminishing S and F of the system. For systems experiencing Synergy F increase while S decreases. Both phenomena are called self-organized emergent order but one process describes equilibrium thermodynamics whereas the other describes far from equilibrium dissipative structure. Thus, the term selforganization is too general to be useful. Here I use the term emergence in the sense that synergetic processes allow novel properties to emerge.
In physics, emergence is the phenomenon of a complex system exhibiting properties that are not present in any of its individual parts. For example, a colony of ants can exhibit emergent behavior such as collective foraging, even though each individual ant is simply following its own instincts. This is also true for energy and entropy. In many complex systems with multiple types of energy, F and S can be hard to measure. Some kind of energy is an emergent phenomena of the interactions of other types of energy. A chain of emergent systems can be envisioned as follows: The atom Subatomic particles assemble to form atoms. Quantum mechanics and nuclear physics are in charge of studying these processes. Nuclear forces and electromagnetic interactions are involved in these processes.

From atoms to molecules
Atoms form chemical bonds between them producing ensembles of atoms called chemical compounds. Chemistry is the science studying these emergent phenomena. Here, nuclear forces play a negligible role and electromagnetic forces are prevalent.

From molecules to cells
Molecules aggregate in complex ways with a high degree of structural information to form biological cells. Cell biology and biochemistry is in charge of studying these emergent phenomena. Mechanical and chemical forces are prevalent in the functioning of these systems.

The working of catalysts
As a fundamental part of the interactions of molecules and cells in achieving emergent phenomena are catalysts, a special science is dedicated to study them. These catalysts are able to direct mechanical and electromagnetic forces to a small part of the system allowing for the appearance of modulation of free energy by structural information. They achieve this by Qeios,.0 · Article, July 2, 2023 Qeios ID: S90ADN.5 · https://doi.org/10.32388/S90ADN.5 17/23 providing spatial-temporal information so as to synchronize processes and reactions that allow synergies to emerge.

From cell to organisms
Cells aggregate in complex ways with a high degree of structural information to form multicellular organisms. Medicine and organismic biology studies them. Organisms develop cellular systems (brains for example) that form networks of neurons that can store and process information in ways a single cell can not. Cells and organisms of different kinds can form functional groupings called Holobionts, or can assemble to form ever more complex systems.

From organisms to society and ecosystems
Sociology and sociobiology study the emergent properties of groups of organisms. Ecologists study the emergent properties of groups of diverse types of organisms. Here, layers of different structural information guide mechanisms to harness free energy of diverse forms. Some of these emergent forms are forces and energies that emerge from interactions of these at lower levels (The most recent paper is Watson & Levin 2023). So we can speak of social and/or ecological forces that are products of myriads of interactions of subsystems. But such forces, even if they are emergent, can be measured and their effect on other systems can be monitored. Social networks store and process information in much larger amounts than individual organisms can, allowing the emergence of culture. Culture can produce machines to store and use information such as computers.

The emergence of emotions
The interaction between perceived signal from outside of our organism, with neurophysiological signals, activating networks of neurons and glia, such as action potential of neurons, filtered transmission of neuronal communication, and hormones that communicate with all parts of our body, are perceived by or proprioceptor producing feelings, some of which we call emotions. The emergent psychological forces are the drivers of behaviors and drive the production of new levels of information. Love is a complex emotion that emerges from the interaction of many factors, including memory, physiology, motivation, culture, personal experience, and more. It is essential for the formation of strong, lasting bonds between people, which in turn are necessary for the survival and successful development of offspring. Love uses information to increase free energy and free energy is needed to acquire more information. In colloquial words, Love requires us to invest energy in our relationships, but this investment pays off in the long run by increasing our psychological and material well-being. Love has its evolutionary origins in biological reproduction, but it has expanded its role in human society. In addition to promoting reproduction, love can also foster creativity, innovation, and other adaptive behaviors. This is because love taps into the same instinctive and cognitive tools that we use for mate selection.

The emergence of conscience
With neural networks and social networks new possibilities emerge, the mind for example (The most recent paper is Levin 2023). The interactions of hormones with physio-electric signals, emotions, neuronal memory, anatomical memory, Each level of complexity draws upon other levels of less complexity. Any science studying the interaction between levels of complexity must be aware that jumping between levels that are far apart, huge errors in the interpretation of the knowledge between the different sciences studying each level will emerge. Two examples show that such inter-level extrapolation in science risks misleading us. Trying to explain consciousness using only knowledge from quantum mechanics, for example, without ensuring consilience between the sciences studying the intermediate levels of complexity (Wilson 1997), is sure to produce more noise than knowledge and is best left to charlatans. The other example is economics. It is clearly a multidimensional dynamic system. Trying to explain economic behavior using simple models such as Rational Utility Functions, or even apparently more sophisticated tools of experimental economics such as "The Prisoner's Dilemma", without attending for emotional dimensions, expectations, social positioning, past experience, moral dimension, learned attitudes towards strangers, and elements studied by sociobiological ethology, is a dysfunctional approach most likely to produce only noise.
A difference regarding information between the various levels of emergent complexity is the type of structural information relevant to produce free energy in each case. The curious fact expressed in a proposition for a fourth law of thermodynamics, is that at all these levels, increases in free energy are always associated with increases in information (Jaffe 2023). This is true for processes occurring in open systems that are far from thermodynamic equilibrium. This relationship between information and energy drives synergies that produce unexpected results, and often new dimensions of organization emerge.

Energy, Information and Emergence
Summarizing our proposition we redefine: Emergence is the phenomenon whereby complex systems exhibit properties that are not present in their individual components, and it provides a framework for understanding the effect of information on the production of free energy in the system, including those of living systems.
Infodynamics. Complex multi-component systems increase their free energy by discovering novel ways for their component parts to interact between them and with their environment. Novel ways that unleash synergies that augment the free energy of the system will be selected by evolutionary processes of natural selection. Thus, the concept of fitness in evolutionary biology actually refers to a free energy or useful energy in terms of the survival of an organism or gene pool. These novel ways represent new information that must be stored and transmitted for future interaction of the system.
However, there is no theoretical recipe to discover useful information. Only by empirically finding that the information produces free energy is that we know it is useful. In evolutionary terms, complex systems need heuristic mechanisms to produce information which then is selected according to its usefulness, or discarded if shown to be noise.
Thermodynamics, information theory, and emergence are all interconnected but not in a straightforward way. We can summarize our exercise the conceptual decantation of this relationship to the formula: where k 1 and k 2 are constants to be assessed experimentally This means that we have two coupled realities: that of thermodynamics and that of infodynamics, and both are transformed by emergence. The different types of energy (E i ) and of information (I i ) in multidimensional systems have to be identified in order to understand this dynamic relationship. No theoretical guide for it exists today but only empirical exploration helps in this identification. To advance we need more efforts in bridging the communication gap between the different disciplines involved in studying these phenomena so as to accelerate the growth of knowledge we have about these concepts and make them more useful for eventual practical and theoretical implementations.
Useful information increase (ΔΦ>0) produces increments in free energy (ΔF >0). As ΔF helps access more information, as evolutionary processes powered by natural selection achieve ever more Φ, more F is possible. Increases in entropy (ΔS>0) decreases free energy (ΔF <0) and might affect the amount of useful information available in the system (Δ Φ<0).
Increases in entropy (ΔS>0) decreases free energy (ΔF <0) and might affect the amount of useful information available in the system (ΔΦ<0). More noise or misleading information (ΔN>0) decreases useful information (ΔΦ<0) which decreases Qeios,.0 · Article, July 2, 2023 Qeios ID: S90ADN.5 · https://doi.org/10.32388/S90ADN.5 20/23 free energy (ΔF<0) These complex relationships help us to better understand the evolution of life, societies and ecosystems and makes the creation of independent artificial life feasible. Analogous explanations for this phenomena include what has been referred to as The Edge of Chaos (Packard 1988) and Autopoiesis (Maturana & Varela 1991). I believe the rationale exposed here is easier to operationalize.
Research can identify changes in useful information (ΔΦ), producing changes in free energy (ΔF), quantify their relationship in different complex, open, far from equilibrium systems, and identify modulators and constraints of this relationship. This may help in focusing on relevant features of these complex systems. What we know so far is that the proposed law for far-from-equilibrium thermodynamics (Jaffe 2023) has many examples to support it and has not been shown to be false so far. The present conceptual clarification might help in eventually falsifying this proposal. A better understanding of information might allow us to deduce this proposed rule from other more fundamental laws. Despite very broad impressive empirical knowledge in many disciplines, we have only a very superficial grasp of the relationship between information and work. Or in abstract terms between ΔF and ΔΦ. Research in the relation between infodynamics and thermodynamics can change our future!