Entropy and Entropy Production: Old Misconceptions and New Breakthroughs

The Relationship Between Astronomical and Developmental Times Emerging in Modeling the Evolution of Agents

The simplest evolutionary model for catching prey by an agent (predator) is considered. The simulation is performed on the basis of a software-emulated Intel i8080 processor. Maximizing the number of catches is chosen as the objective function. This function is associated with energy dissipation and developmental time. It is shown that during Darwinian evolution, agents with an initially a random set of processor commands subsequently acquire a successful catching skill. It is found that in the process of evolution, a logarithmic relationship between astronomical and developmental times arises in agents. This result is important for the ideas available in the literature about the close connection of such concepts as time, Darwinian selection, and the maximization of entropy production.

Maximization of entropy production during vibration in a suspension based on graphite and silicone oil

The electrical conductivity of a suspension of graphite and silicone oil in the presence of a small electric potential difference and vibration (40÷50Hz) is considered. The concentration of the suspension was selected near the percolation threshold. It has been found that such a nonequilibrium system evolves to increase its dissipation power, and low-energy vibrations accelerate, and high-energy ones hinder this process. Since the dissipation power of the considered system is proportional to entropy production, the results obtained are consistent with the so-called maximum entropy production principle (MEPP). This is the first experimental confirmation of MEPP in the case of a nonequilibrium process with continuous transformations under conditions for the emergence of alternative variants for the development. The possibility of choice among alternatives in a complex system is a fundamental point in the experimental discussion of MEPP, and it was previously underestimated.

Irreversibility in belief dynamics: Unraveling the link to cognitive effort

The relationship between time irreversibility in neuronal dynamics and cognitive effort is a subject of growing interest in the scientific literature. Although correlations between proxies of both concepts have been experimentally observed, the underlying precise linkage between them remains elusive. Here we investigate the case of learning in decision-making tasks; we do so by introducing a thermodynamically grounded metric-inspired by Landauer's principle-which connects time-irreversible information processing to energy consumption. Equipped with this metric, we investigate the role of macroscopic time-reversal symmetry breaking in belief dynamics for the case of an agent with finite sensitivity while performing a static two-armed bandit task-a standard setup in cognitive neuroscience. To gain insights into the belief dynamics, we analogize it to the dynamics of an active particle subject to state-dependent noise and living in a two-dimensional space. This mapping allows an analytical description of learning-induced biases. We deeply explore the case of Q-learning with forgetting the nonchosen option. In this case, learning-induced risk aversion is formally equivalent to standard thermophoresis, i.e., the net motion towards low-temperature regions. Finally, we quantify the irreversibility of belief dynamics in the steady state for different bandit configurations, sensitivity levels, and exploitative behavior. We found a strong correlation in high-sensitivity learning between heightened irreversibility in belief dynamics and improved decision-making outcomes. Notably, as the task's difficulty increases, a greater degree of irreversibility in belief dynamics becomes necessary for having superior performances; this explicitly unravels a plausible connection between time irreversibility and cognitive effort. In conclusion, our investigation reveals that irreversibility in belief dynamics bridges out-of-equilibrium statistical physics concepts and cognitive neuroscience. In decision-making contexts, this perspective offers insights into the notion of cognitive effort, suggesting a potential mechanism driving the evolution of living systems toward out-of-equilibrium structures.

Bio-analog dissipative structures and principles of biological behavior

The place of living organisms in the natural world is a nearly perennial question in philosophy and the sciences; how can inanimate matter yield animate beings? A dominant answer for several centuries has been to treat organisms as sophisticated machines, studying them with the mechanistic physics and chemistry that have given rise to technology and complex machines. Since the early 20th century, many scholars have sought instead to naturalize biology through thermodynamics, recognizing the precarious far-from-equilibrium state of organisms. Erwin Bauer was an early progenitor of this perspective with ambitions of "general laws for the movement of living matter". In addition to taking a thermodynamic perspective, Bauer recognized that organisms are fundamentally behaving systems, and that explaining the physics of life requires explaining the origins of intentionality, adaptability, and self-regulation. Bauer, like some later scholars, seems to advocate for a "new physics", one that extends beyond mechanics and classical thermodynamic, one that would be inclusive of living systems. In this historical review piece, we explore some of Bauer's ideas and explain how similar concepts have been explored in modern non-equilibrium thermodynamics and dissipative structure theory. Non-living dissipative structures display end-directedness, self-maintenance, and adaptability analogous to organisms. These findings also point to an alternative framework for the life sciences, that treats organisms not as machines but as sophisticated dissipative structures. We evaluate the differences between mechanistic and thermodynamic perspectives on life, and what each theory entails for understanding the behavior of organisms.

Theoretical Improvements in Enzyme Efficiency Associated with Noisy Rate Constants and Increased Dissipation

Previous studies have revealed the extraordinarily large catalytic efficiency of some enzymes. High catalytic proficiency is an essential accomplishment of biological evolution. Natural selection led to the increased turnover number, kcat, and enzyme efficiency, kcat/KM, of uni-uni enzymes, which convert a single substrate into a single product. We added or multiplied random noise with chosen rate constants to explore the correlation between dissipation and catalytic efficiency for ten enzymes: beta-galactosidase, glucose isomerase, β-lactamases from three bacterial strains, ketosteroid isomerase, triosephosphate isomerase, and carbonic anhydrase I, II, and T200H. Our results highlight the role of biological evolution in accelerating thermodynamic evolution. The catalytic performance of these enzymes is proportional to overall entropy production-the main parameter from irreversible thermodynamics. That parameter is also proportional to the evolutionary distance of β-lactamases PC1, RTEM, and Lac-1 when natural or artificial evolution produces the optimal or maximal possible catalytic efficiency. De novo enzyme design and attempts to speed up the rate-limiting catalytic steps may profit from the described connection between kinetics and thermodynamics.

Energy conversion theorems for some linear steady states

One of the main issues that real energy converters present, when they produce effective work, is the inevitable entropy production. Within the context of nonequilibrium thermodynamics, entropy production tends to energetically degrade human-made or living systems. On the other hand, it is not useful to think about designing an energy converter that works in the so-called minimum entropy production regime since the effective power output and efficiency are zero. In this paper we establish some energy conversion theorems similar to Prigogine's theorem with constrained forces. The purpose of these theorems is to reveal trade-offs between design and the so-called operation modes for (2×2)-linear isothermal energy converters. The objective functions that give rise to those thermodynamic constraints show stability. A two-mesh electric circuit was built as an example to demonstrate the theorems' validity. Likewise, we reveal a type of energetic hierarchy for power output, efficiency, and dissipation function when the circuit is tuned to any of the operating regimes studied here. These are maximum power output (MPO), maximum efficient power (MPη), maximum omega function (MΩ), maximum ecological function (MEF), maximum efficiency (Mη), and minimum dissipation function (mdf).

Is Darwinian selection a retrograde driving force of evolution?

Modern science has still not provided a satisfactory empirical explanation for the increasing complexity of living organisms through evolutionary history. As no agreed-upon definitions of the complexity exist, the working definition of biological complexity has been formulated. There is no theoretical reason to expect evolutionary lineages to increase in complexity over time, and there is no empirical evidence that they do so. In our discussion we have assumed the hypothesis that at the origins of life, evolution had to first involve autocatalytic systems that only subsequently acquired the capacity of genetic heredity. We discuss the role of Darwinian selection in evolution and pose the hypothesis that Darwinian selection acts predominantly as a retrograde driving force of evolution. In this context we understand the term retrograde evolution as a degeneration of living systems from higher complexity towards living systems with lower complexity. With the proposed hypothesis we have closed the gap between Darwinism and Lamarckism early in the evolutionary process. By Lamarckism, the action of a special principle called complexification force is understood here rather than inheritance of acquired characteristics.

A Quantum-like Model of Interdependence for Embodied Human-Machine Teams: Reviewing the Path to Autonomy Facing Complexity and Uncertainty

In this review, our goal is to design and test quantum-like algorithms for Artificial Intelligence (AI) in open systems to structure a human-machine team to be able to reach its maximum performance. Unlike the laboratory, in open systems, teams face complexity, uncertainty and conflict. All task domains have complexity levels-some low, and others high. Complexity in this new domain is affected by the environment and the task, which are both affected by uncertainty and conflict. We contrast individual and interdependence approaches to teams. The traditional and individual approach focuses on building teams and systems by aggregating the best available information for individuals, their thoughts, behaviors and skills. Its concepts are characterized chiefly by one-to-one relations between mind and body, a summation of disembodied individual mental and physical attributes, and degrees of freedom corresponding to the number of members in a team; however, this approach is characterized by the many researchers who have invested in it for almost a century with few results that can be generalized to human-machine interactions; by the replication crisis of today (e.g., the invalid scale for self-esteem); and by its many disembodied concepts. In contrast, our approach is based on the quantum-like nature of interdependence. It allows us theorization about the bistability of mind and body, but it poses a measurement problem and a non-factorable nature. Bistability addresses team structure and performance; the measurement problem solves the replication crisis; and the non-factorable aspect of teams reduces the degrees of freedom and the information derivable from teammates to match findings by the National Academies of Science. We review the science of teams and human-machine team research in the laboratory versus in the open field; justifications for rejecting traditional social science while supporting our approach; a fuller understanding of the complexity of teams and tasks; the mathematics involved; a review of results from our quantum-like model in the open field (e.g., tradeoffs between team structure and performance); and the path forward to advance the science of interdependence and autonomy.

The Entropy of Entropy: Are We Talking about the Same Thing?

In the last few decades, the number of published papers that include search terms such as thermodynamics, entropy, ecology, and ecosystems has grown rapidly. Recently, background research carried out during the development of a paper on "thermodynamics in ecology" revealed huge variation in the understanding of the meaning and the use of some of the central terms in this field-in particular, entropy. This variation seems to be based primarily on the differing educational and scientific backgrounds of the researchers responsible for contributions to this field. Secondly, some ecological subdisciplines also seem to be better suited and applicable to certain interpretations of the concept than others. The most well-known seems to be the use of the Boltzmann-Gibbs equation in the guise of the Shannon-Weaver/Wiener index when applied to the estimation of biodiversity in ecology. Thirdly, this tendency also revealed that the use of entropy-like functions could be diverted into an area of statistical and distributional analyses as opposed to real thermodynamic approaches, which explicitly aim to describe and account for the energy fluxes and dissipations in the systems. Fourthly, these different ways of usage contribute to an increased confusion in discussions about efficiency and possible telos in nature, whether at the developmental level of the organism, a population, or an entire ecosystem. All the papers, in general, suffer from a lack of clear definitions of the thermodynamic functions used, and we, therefore, recommend that future publications in this area endeavor to achieve a more precise use of language. Only by increasing such efforts it is possible to understand and resolve some of the significant and possibly misleading discussions in this area.

The Time Evolution of Mutual Information between Disjoint Regions in the Universe

We study the time evolution of mutual information between mass distributions in spatially separated but casually connected regions in an expanding universe. The evolution of mutual information is primarily determined by the configuration entropy rate, which depends on the dynamics of the expansion and growth of density perturbations. The joint entropy between distributions from the two regions plays a negligible role in such evolution. Mutual information decreases with time in a matter-dominated universe, whereas it stays constant in a Λ-dominated universe. The ΛCDM model and some other models of dark energy predict a minimum in mutual information beyond which dark energy dominates the dynamics of the universe. Mutual information may have deeper connections to the dark energy and accelerated expansion of the universe.

Self-Organization of Enzyme-Catalyzed Reactions Studied by the Maximum Entropy Production Principle

The self-organization of open reaction systems is closely related to specific mechanisms that allow the export of internally generated entropy from systems to their environment. According to the second law of thermodynamics, systems with effective entropy export to the environment are better internally organized. Therefore, they are in thermodynamic states with low entropy. In this context, we study how self-organization in enzymatic reactions depends on their kinetic reaction mechanisms. Enzymatic reactions in an open system are considered to operate in a non-equilibrium steady state, which is achieved by satisfying the principle of maximum entropy production (MEPP). The latter is a general theoretical framework for our theoretical analysis. Detailed theoretical studies and comparisons of the linear irreversible kinetic schemes of an enzyme reaction in two and three states are performed. In both cases, in the optimal and statistically most probable thermodynamic steady state, a diffusion-limited flux is predicted by MEPP. Several thermodynamic quantities and enzymatic kinetic parameters, such as the entropy production rate, the Shannon information entropy, reaction stability, sensitivity, and specificity constants, are predicted. Our results show that the optimal enzyme performance may strongly depend on the number of reaction steps when linear reaction mechanisms are considered. Simple reaction mechanisms with a smaller number of intermediate reaction steps could be better organized internally and could allow fast and stable catalysis. These could be features of the evolutionary mechanisms of highly specialized enzymes.

The Conditions Necessary for the Formation of Dissipative Structures in Tribo-Films on Friction Surfaces That Decrease the Wear Rate

Tribo-films form on surfaces as a result of friction and wear. The wear rate is dependent on the frictional processes, which develop within these tribo-films. Physical-chemical processes with negative entropy production enhance reduction in the wear rate. Such processes intensively develop once self-organization with dissipative structure formation is initiated. This process leads to significant wear rate reduction. Self-organization can only occur after the system loses thermodynamic stability. This article investigates the behavior of entropy production that results in the loss of thermodynamic stability in order to establish the prevalence of friction modes required for self-organization. Tribo-films with dissipative structures form on the friction surface as a consequence of a self-organization process, resulting in an overall wear rate reduction. It has been demonstrated that a tribo-system begins to lose its thermodynamic stability once it reaches the point of maximum entropy production during the running-in stage.

Is the tendency to maximise energy distribution an optimal collective activity for biological purposes? A proposal for a global principle of biological organization

Our purpose is to address the biological problem of finding foundations of the organization in the collective activity among cell networks in the nervous system, at the meso/macroscale, giving rise to cognition and consciousness. But in doing so, we encounter another problem related to the interpretation of methods to assess the neural interactions and organization of the neurodynamics, because thermodynamic notions, which have precise meaning only under specific conditions, have been widely employed in these studies. The consequence is that apparently contradictory results appear in the literature, but these contradictions diminish upon the considerations of the specific circumstances of each experiment. After clarifying some of these controversial points and surveying some experimental results, we propose that a necessary condition for cognition/consciousness to emerge is to have available enough energy, or cellular activity; and a sufficient condition is the multiplicity of configurations in which cell networks can communicate, resulting in non-uniform energy distribution, the generation and dissipation of energy gradients due to the constant activity. The diversity of sensorimotor processing of higher animals needs a flexible, fluctuating web on neuronal connections, and we review results supporting such multiplicity of configurations among brain regions associated with conscious awareness and healthy brain states. These ideas may reveal possible fundamental principles of brain organization that could be extended to other natural phenomena and how healthy activity may derive to pathological states.

Foraging Dynamics and Entropy Production in a Simulated Proto-Cell

All organisms depend on a supply of energetic resources to power behavior and the irreversible entropy-producing processes that sustain them. Dissipative structure theory has often been a source of inspiration for better understanding the thermodynamics of biology, yet real organisms are inordinately more complex than most laboratory systems. Here we report on a simulated chemical dissipative structure that operates as a proto cell. The simulated swimmer moves through a 1D environment collecting resources that drive a nonlinear reaction network interior to the swimmer. The model minimally represents properties of a simple organism including rudimentary foraging and chemotaxis and an analog of a metabolism in the nonlinear reaction network. We evaluated how dynamical stability of the foraging dynamics (i.e., swimming and chemotaxis) relates to the rate of entropy production. Results suggested a relationship between dynamical steady states and entropy production that was tuned by the relative coordination of foraging and metabolic processes. Results include evidence in support of and contradicting one formulation of a maximum entropy production principle. We discuss the status of this principle and its relevance to biology.

Interdependent Autonomous Human-Machine Systems: The Complementarity of Fitness, Vulnerability and Evolution

For the science of autonomous human-machine systems, traditional causal-time interpretations of reality in known contexts are sufficient for rational decisions and actions to be taken, but not for uncertain or dynamic contexts, nor for building the best teams. First, unlike game theory where the contexts are constructed for players, or machine learning where contexts must be stable, when facing uncertainty or conflict, a rational process is insufficient for decisions or actions to be taken; second, as supported by the literature, rational explanations cannot disaggregate human-machine teams. In the first case, interdependent humans facing uncertainty spontaneously engage in debate over complementary tradeoffs in a search for the best path forward, characterized by maximum entropy production (MEP); however, in the second case, signified by a reduction in structural entropy production (SEP), interdependent team structures make it rationally impossible to discern what creates better teams. In our review of evidence for SEP-MEP complementarity for teams, we found that structural redundancy for top global oil producers, replicated for top global militaries, impedes interdependence and promotes corruption. Next, using UN data for Middle Eastern North African nations plus Israel, we found that a nation's structure of education is significantly associated with MEP by the number of patents it produces; this conflicts with our earlier finding that a U.S. Air Force education in air combat maneuvering was not associated with the best performance in air combat, but air combat flight training was. These last two results exemplify that SEP-MEP interactions by the team's best members are made by orthogonal contributions. We extend our theory to find that competition between teams hinges on vulnerability, a complementary excess of SEP and reduced MEP, which generalizes to autonomous human-machine systems.

Entropy Perspectives of Molecular and Evolutionary Biology

Attempts to find and quantify the supposed low entropy of organisms and its preservation are revised. The absolute entropy of the mixed components of non-living biomass (approximately −1.6 × 10³ J K⁻¹ L⁻¹) is the reference to which other entropy decreases would be ascribed to life. The compartmentation of metabolites and the departure from the equilibrium of metabolic reactions account for reductions in entropy of 1 and 40–50 J K⁻¹ L⁻¹, respectively, and, though small, are distinctive features of living tissues. DNA and proteins do not supply significant decreases in thermodynamic entropy, but their low informational entropy is relevant for life and its evolution. No other living feature contributes significantly to the low entropy associated with life. The photosynthetic conversion of radiant energy to biomass energy accounts for most entropy (2.8 × 10⁵ J K⁻¹ carbon kg⁻¹) produced by living beings. The comparatively very low entropy produced in other processes (approximately 4.8 × 10² J K⁻¹ L⁻¹ day⁻¹ in the human body) must be rapidly exported outside as heat to preserve low entropy decreases due to compartmentation and non-equilibrium metabolism. Enzymes and genes are described, whose control minimizes the rate of production of entropy and could explain selective pressures in biological evolution and the rapid proliferation of cancer cells.

Entropy: From Thermodynamics to Information Processing

Entropy is a concept that emerged in the 19th century. It used to be associated with heat harnessed by a thermal machine to perform work during the Industrial Revolution. However, there was an unprecedented scientific revolution in the 20th century due to one of its most essential innovations, i.e., the information theory, which also encompasses the concept of entropy. Therefore, the following question is naturally raised: “what is the difference, if any, between concepts of entropy in each field of knowledge?” There are misconceptions, as there have been multiple attempts to conciliate the entropy of thermodynamics with that of information theory. Entropy is most commonly defined as “disorder”, although it is not a good analogy since “order” is a subjective human concept, and “disorder” cannot always be obtained from entropy. Therefore, this paper presents a historical background on the evolution of the term “entropy”, and provides mathematical evidence and logical arguments regarding its interconnection in various scientific areas, with the objective of providing a theoretical review and reference material for a broad audience.

Continuous nonequilibrium transition driven by heat flow

We discovered an out-of-equilibrium transition in the ideal gas between two walls, divided by an inner, adiabatic, movable wall. The system is driven out-of-equilibrium by supplying energy directly into the volume of the gas. At critical heat flux we have found a continuous transition to the state with a low-density, hot gas on one side of the movable wall and a dense, cold gas on the other side. Molecular dynamic simulations of the soft-sphere fluid confirm the existence of the transition in the interacting system. We introduce a stationary state Helmholtz-like function whose minimum determines the stable positions of the internal wall. This transition can be used as a paradigm of transitions in stationary states and the Helmholtz-like function as a paradigm of the thermodynamic description of these states.

Principle of Least Effort and Sentence Length in Public Speaking

The analysis of sentence lengths in the inaugural speeches of US presidents and the annual speeches of UK party leaders is carried out. Transcripts of the speeches are used, rather than the oral production. It is discovered that the average sentence length in these speeches decreases linearly with time, with the slope of 0.13 ± 0.03 words/year. It is shown that among the analyzed distributions (log-normal, folded and half normal, Weibull, generalized Pareto, Rayleigh) the Weibull is the best distribution for describing sentence length. These two results can be considered a consequence of the principle of least effort. The connection of this principle with the well-known principles of maximum and minimum entropy production is discussed.

An Evolution Based on Various Energy Strategies

The simplest model of the evolution of agents with different energy strategies is considered. The model is based on the most general thermodynamic ideas and includes the procedures for selection, inheritance, and variability. The problem of finding a universal strategy (principle) as a selection of possible competing strategies is solved. It is shown that when there is non-equilibrium between the medium and agents, a direction in the evolution of agents arises, but at the same time, depending on the conditions of the evolution, different strategies can be successful. However, for this case, the simulation results reveal that in the presence of significant competition of agents, the strategy that has the maximum total energy dissipation of agents arising as a result of evolution turns out to be successful. Thus, it is not the specific strategy that is universal, but the maximization of dissipation. This result discovers an interesting connection between the basic principles of Darwin–Wallace evolution and the maximum entropy production principle.

Exploring the Interdependence Theory of Complementarity with Case Studies. Autonomous Human–Machine Teams (A-HMTs)

Rational models of human behavior aim to predict, possibly control, humans. There are two primary models, the cognitive model that treats behavior as implicit, and the behavioral model that treats beliefs as implicit. The cognitive model reigned supreme until reproducibility issues arose, including Axelrod’s prediction that cooperation produces the best outcomes for societies. In contrast, by dismissing the value of beliefs, predictions of behavior improved dramatically, but only in situations where beliefs were suppressed, unimportant, or in low risk, highly certain environments, e.g., enforced cooperation. Moreover, rational models lack supporting evidence for their mathematical predictions, impeding generalizations to artificial intelligence (AI). Moreover, rational models cannot scale to teams or systems, which is another flaw. However, the rational models fail in the presence of uncertainty or conflict, their fatal flaw. These shortcomings leave rational models ill-prepared to assist the technical revolution posed by autonomous human–machine teams (A-HMTs) or autonomous systems. For A-HMT teams, we have developed the interdependence theory of complementarity, largely overlooked because of the bewilderment interdependence causes in the laboratory. Where the rational model fails in the face of uncertainty or conflict, interdependence theory thrives. The best human science teams are fully interdependent; intelligence has been located in the interdependent interactions of teammates, and interdependence is quantum-like. We have reported in the past that, facing uncertainty, human debate exploits the interdependent bistable views of reality in tradeoffs seeking the best path forward. Explaining uncertain contexts, which no single agent can determine alone, necessitates that members of A-HMTs express their actions in causal terms, however imperfectly. Our purpose in this paper is to review our two newest discoveries here, both of which generalize and scale, first, following new theory to separate entropy production from structure and performance, and second, discovering that the informatics of vulnerability generated during competition propels evolution, invisible to the theories and practices of cooperation.

An Evolutionary Perspective of Dyslexia, Stress, and Brain Network Homeostasis

Evolution fuels interindividual variability in neuroplasticity, reflected in brain anatomy and functional connectivity of the expanding neocortical regions subserving reading ability. Such variability is orchestrated by an evolutionarily conserved, competitive balance between epigenetic, stress-induced, and cognitive-growth gene expression programs. An evolutionary developmental model of dyslexia, suggests that prenatal and childhood subclinical stress becomes a risk factor for dyslexia when physiological adaptations to stress promoting adaptive fitness, may attenuate neuroplasticity in the brain regions recruited for reading. Stress has the potential to blunt the cognitive-growth functions of the predominantly right hemisphere Ventral and Dorsal attention networks, which are primed with high entropic levels of synaptic plasticity, and are critical for acquiring beginning reading skills. The attentional networks, in collaboration with the stress-responsive Default Mode network, modulate the entrainment and processing of the low frequency auditory oscillations (1-8 Hz) and visuospatial orienting linked etiologically to dyslexia. Thus, dyslexia may result from positive, but costly adaptations to stress system dysregulation: protective measures that reset the stress/growth balance of processing to favor the Default Mode network, compromising development of the attentional networks. Such a normal-variability conceptualization of dyslexia is at odds with the frequent assumption that dyslexia results from a neurological abnormality. To put the normal-variability model in the broader perspective of the state of the field, a traditional evolutionary account of dyslexia is presented to stimulate discussion of the scientific merits of the two approaches.

The thermodynamics of cognition: A mathematical treatment

There is a general expectation that the laws of classical physics must apply to biology, particularly the neural system. The evoked cycle represents the brain's energy/information exchange with the physical environment through stimulus. Therefore, the thermodynamics of emotions might elucidate the neurological origin of intellectual evolution, and explain the psychological and health consequences of positive and negative emotional states based on their energy profiles. We utilized the Carnot cycle and Landauer's principle to analyze the energetic consequences of the brain's resting and evoked states during and after various cognitive states. Namely, positive emotional states can be represented by the reversed Carnot cycle, whereas negative emotional reactions trigger the Carnot cycle. The two conditions have contrasting energetic and entropic aftereffects with consequences for mental energy. The mathematics of the Carnot and reversed Carnot cycles, which can explain recent findings in human psychology, might be constructive in the scientific endeavor in turning psychology into hard science.

Why is Complexity Science valuable for reaching the goals of the UN 2030 Agenda?

The goals and targets included in the 2030 Agenda compiled by the United Nations want to stimulate action in areas of critical importance for humanity and the Earth. These goals and targets regard everyone on Earth from both the health and economic and social perspectives. Reaching these goals means to deal with Complex Systems. Therefore, Complexity Science is undoubtedly valuable. However, it needs to extend its scope and focus on some specific objectives. This article proposes a development of Complexity Science that will bring benefits for achieving the United Nations' aims. It presents a list of the features shared by all the Complex Systems involved in the 2030 Agenda. It shows the reasons why there are certain limitations in the prediction of Complex Systems' behaviors. It highlights that such limitations raise ethical issues whenever new technologies interfere with the dynamics of Complex Systems, such as human beings and the environment. Finally, new methodological approaches and promising research lines to face Complexity Challenges included in the 2030 Agenda are put forward.

Quantum-Like Interdependence Theory Advances Autonomous Human-Machine Teams (A-HMTs)

As humanity grapples with the concept of autonomy for human–machine teams (A-HMTs), unresolved is the necessity for the control of autonomy that instills trust. For non-autonomous systems in states with a high degree of certainty, rational approaches exist to solve, model or control stable interactions; e.g., game theory, scale-free network theory, multi-agent systems, drone swarms. As an example, guided by artificial intelligence (AI, including machine learning, ML) or by human operators, swarms of drones have made spectacular gains in applications too numerous to list (e.g., crop management; mapping, surveillance and fire-fighting systems; weapon systems). But under states of uncertainty or where conflict exists, rational models fail, exactly where interdependence theory thrives. Large, coupled physical or information systems can also experience synergism or dysergism from interdependence. Synergistically, the best human teams are not only highly interdependent, but they also exploit interdependence to reduce uncertainty, the focus of this work-in-progress and roadmap. We have long argued that interdependence is fundamental to human autonomy in teams. But for A-HMTs, no mathematics exists to build from rational theory or social science for their design nor safe or effective operation, a severe weakness. Compared to the rational and traditional social theory, we hope to advance interdependence theory first by mapping similarities between quantum theory and our prior findings; e.g., to maintain interdependence, we previously established that boundaries reduce dysergic effects to allow teams to function (akin to blocking interference to prevent quantum decoherence). Second, we extend our prior findings with case studies to predict with interdependence theory that as uncertainty increases in non-factorable situations for humans, the duality in two-sided beliefs serves debaters who explore alternatives with tradeoffs in the search for the best path going forward. Third, applied to autonomous teams, we conclude that a machine in an A-HMT must be able to express itself to its human teammates in causal language however imperfectly.

Optimizing Our Patients' Entropy Production as Therapy? Hypotheses Originating from the Physics of Physiology

Understanding how nature drives entropy production offers novel insights regarding patient care. Whilst energy is always preserved and energy gradients irreversibly dissipate (thus producing entropy), increasing evidence suggests that they do so in the most optimal means possible. For living complex non-equilibrium systems to create a healthy internal emergent order, they must continuously produce entropy over time. The Maximum Entropy Production Principle (MEPP) highlights nature's drive for non-equilibrium systems to augment their entropy production if possible. This physical drive is hypothesized to be responsible for the spontaneous formation of fractal structures in space (e.g., multi-scale self-similar tree-like vascular structures that optimize delivery to and clearance from an organ system) and time (e.g., complex heart and respiratory rate variability); both are ubiquitous and essential for physiology and health. Second, human entropy production, measured by heat production divided by temperature, is hypothesized to relate to both metabolism and consciousness, dissipating oxidative energy gradients and reducing information into meaning and memory, respectively. Third, both MEPP and natural selection are hypothesized to drive enhanced functioning and adaptability, selecting states with robust basilar entropy production, as well as the capacity to enhance entropy production in response to exercise, heat stress, and illness. Finally, a targeted focus on optimizing our patients' entropy production has the potential to improve health and clinical outcomes. With the implications of developing a novel understanding of health, illness, and treatment strategies, further exploration of this uncharted ground will offer value.

Thermodynamics in Ecology-An Introductory Review

How to predict the evolution of ecosystems is one of the numerous questions asked of ecologists by managers and politicians. To answer this we will need to give a scientific definition to concepts like sustainability, integrity, resilience and ecosystem health. This is not an easy task, as modern ecosystem theory exemplifies. Ecosystems show a high degree of complexity, based upon a high number of compartments, interactions and regulations. The last two decades have offered proposals for interpretation of ecosystems within a framework of thermodynamics. The entrance point of such an understanding of ecosystems was delivered more than 50 years ago through Schrödinger's and Prigogine's interpretations of living systems as "negentropy feeders" and "dissipative structures", respectively. Combining these views from the far from equilibrium thermodynamics to traditional classical thermodynamics, and ecology is obviously not going to happen without problems. There seems little reason to doubt that far from equilibrium systems, such as organisms or ecosystems, also have to obey fundamental physical principles such as mass conservation, first and second law of thermodynamics. Both have been applied in ecology since the 1950s and lately the concepts of exergy and entropy have been introduced. Exergy has recently been proposed, from several directions, as a useful indicator of the state, structure and function of the ecosystem. The proposals take two main directions, one concerned with the exergy stored in the ecosystem, the other with the exergy degraded and entropy formation. The implementation of exergy in ecology has often been explained as a translation of the Darwinian principle of "survival of the fittest" into thermodynamics. The fittest ecosystem, being the one able to use and store fluxes of energy and materials in the most efficient manner. The major problem in the transfer to ecology is that thermodynamic properties can only be calculated and not measured. Most of the supportive evidence comes from aquatic ecosystems. Results show that natural and culturally induced changes in the ecosystems, are accompanied by a variations in exergy. In brief, ecological succession is followed by an increase of exergy. This paper aims to describe the state-of-the-art in implementation of thermodynamics into ecology. This includes a brief outline of the history and the derivation of the thermodynamic functions used today. Examples of applications and results achieved up to now are given, and the importance to management laid out. Some suggestions for essential future research agendas of issues that needs resolution are given.

Symmetry of small clusters of levitating water droplets

Self-assembled clusters of condensed water microdroplets can levitate over a locally heated layer of water. Large clusters form hexagonally ordered (honeycomb) structures similar to colloidal crystals, while small (from one to several dozens of droplets) clusters possess special symmetry properties. Small clusters may demonstrate 4-fold, 5-fold, and 7-fold symmetry which is absent from large clusters and crystals. The symmetry properties of small cluster configurations are universal, i.e., they do not depend on the size of the droplets and details of the interactions between the droplets. The small cluster configurations may be compared with other types of symmetric objects in geometry.

Storage of Energy in Constrained Non-Equilibrium Systems

We study a quantity T defined as the energy U, stored in non-equilibrium steady states (NESS) over its value in equilibrium U0, ΔU=U−U0 divided by the heat flow JU going out of the system. A recent study suggests that T is minimized in steady states (Phys.Rev.E.99, 042118 (2019)). We evaluate this hypothesis using an ideal gas system with three methods of energy delivery: from a uniformly distributed energy source, from an external heat flow through the surface, and from an external matter flow. By introducing internal constraints into the system, we determine T with and without constraints and find that T is the smallest for unconstrained NESS. We find that the form of the internal energy in the studied NESS follows U=U0∗f(JU). In this context, we discuss natural variables for NESS, define the embedded energy (an analog of Helmholtz free energy for NESS), and provide its interpretation.

The fourth law of thermodynamics: steepest entropy ascent

When thermodynamics is understood as the science (or art) of constructing effective models of natural phenomena by choosing a minimal level of description capable of capturing the essential features of the physical reality of interest, the scientific community has identified a set of general rules that the model must incorporate if it aspires to be consistent with the body of known experimental evidence. Some of these rules are believed to be so general that we think of them as laws of Nature, such as the great conservation principles, whose 'greatness' derives from their generality, as masterfully explained by Feynman in one of his legendary lectures. The second law of thermodynamics is universally contemplated among the great laws of Nature. In this paper, we show that in the past four decades, an enormous body of scientific research devoted to modelling the essential features of non-equilibrium natural phenomena has converged from many different directions and frameworks towards the general recognition (albeit still expressed in different but equivalent forms and language) that another rule is also indispensable and reveals another great law of Nature that we propose to call the 'fourth law of thermodynamics'. We state it as follows: every non-equilibrium state of a system or local subsystem for which entropy is well defined must be equipped with a metric in state space with respect to which the irreversible component of its time evolution is in the direction of steepest entropy ascent compatible with the conservation constraints. To illustrate the power of the fourth law, we derive (nonlinear) extensions of Onsager reciprocity and fluctuation-dissipation relations to the far-non-equilibrium realm within the framework of the rate-controlled constrained-equilibrium approximation (also known as the quasi-equilibrium approximation). This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

The Interdependence of Autonomous Human-Machine Teams: The Entropy of Teams, But Not Individuals, Advances Science

Key concepts: We review interdependence theory measured by entropic forces, findings in support, and several examples from the field to advance a science of autonomous human-machine teams (A-HMTs) with artificial intelligence (AI). While theory is needed for the advent of autonomous HMTs, social theory is predicated on methodological individualism, a statistical and qualitative science that neither generalizes to human teams nor HMTs. Maximum interdependence in human teams is associated with the performance of the best teams when compared to independent individuals; our research confirmed that the top global oil firms maximize interdependence by minimizing redundant workers, replicated for the top militaries in the world, adding that impaired interdependence is associated with proportionately less freedom, increased corruption, and poorer team performance. We advanced theory by confirming that the maximum interdependence in teams requires intelligence to overcome obstacles to maximum entropy production (MEP; e.g., navigating obstacles while abiding by military rules of engagement requires intelligence). Approach: With a case study, we model as harmonic the long-term oscillations driven by two federal agencies in conflict over closing two high-level radioactive waste tanks, ending when citizens recommended closing the tanks. Results: While contradicting rational consensus theory, our quasi-Nash equilibrium model generates the information for neutrals to decide; it suggests that HMTs should adopt how harmonic oscillations in free societies regulate human autonomy to improve decisions and social welfare.

Entropy Production and Its Application to the Coupled Nonequilibrium Processes of ATP Synthesis

Starting from the universal concept of entropy production, a large number of new results are obtained and a wealth of novel thermodynamic, kinetic, and molecular mechanistic insights are provided into the coupling of oxidation and ATP synthesis in the vital process of oxidative phosphorylation (OX PHOS). The total dissipation, Φ, in OX PHOS with succinate as respiratory substrate is quantified from measurements, and the partitioning of Φ into the elementary components of ATP synthesis, leak, slip, and other losses is evaluated for the first time. The thermodynamic efficiency, η, of the coupled process is calculated from the data on Φ and shown to agree well with linear nonequilibrium thermodynamic calculations. Equations for the P/O ratio based on total oxygen consumed and extra oxygen consumed are derived from first principles and the source of basal (state 4) mitochondrial respiration is postulated from molecular mechanistic considerations based on Nath’s two-ion theory of energy coupling within the torsional mechanism of energy transduction and ATP synthesis. The degree of coupling, q, between oxidation and ATP synthesis is determined from the experimental data and the irreversible thermodynamics analysis. The optimality of biological free energy converters is explored in considerable detail based on (i) the standard biothermodynamic approach, and (ii) a new biothermokinetic approach developed in this work, and an effective solution that is shown to arise from consideration of the molecular aspects in Nath’s theory is formulated. New experimental data in state 4 with uncouplers and redox inhibitors of OX PHOS and on respiratory control in the physiological state 3 with ADP and uncouplers are presented. These experimental observations are shown to be incompatible with Mitchell’s chemiosmotic theory. A novel scheme of coupling based on Nath’s two-ion theory of energy coupling within the torsional mechanism is proposed and shown to explain the data and also pass the test of consistency with the thermodynamics, taking us beyond the chemiosmotic theory. It is concluded that, twenty years since its first proposal, Nath’s torsional mechanism of energy transduction and ATP synthesis is now well poised to catalyze the progress of experimental and theoretical research in this interdisciplinary field.

Maximum Entropy Production Theorem for Transitions between Enzyme Functional States and Its Applications

Transitions between enzyme functional states are often connected to conformational changes involving electron or proton transport and directional movements of a group of atoms. These microscopic fluxes, resulting in entropy production, are driven by non-equilibrium concentrations of substrates and products. Maximal entropy production exists for any chosen transition, but such a maximal transitional entropy production (MTEP) requirement does not ensure an increase of total entropy production, nor an increase in catalytic performance. We examine when total entropy production increases, together with an increase in the performance of an enzyme or bioenergetic system. The applications of the MTEP theorem for transitions between functional states are described for the triosephosphate isomerase, ATP synthase, for β-lactamases, and for the photochemical cycle of bacteriorhodopsin. The rate-limiting steps can be easily identified as those which are the most efficient in dissipating free-energy gradients and in performing catalysis. The last step in the catalytic cycle is usually associated with the highest free-energy dissipation involving proton nanocurents. This recovery rate-limiting step can be optimized for higher efficiency by using corresponding MTEP requirements. We conclude that biological evolution, leading to increased optimal catalytic efficiency, also accelerated the thermodynamic evolution, the synergistic relationship we named the evolution-coupling hypothesis.

Time-Energy and Time-Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations

In the domain of nondissipative unitary Hamiltonian dynamics, the well-known Mandelstam–Tamm–Messiah time–energy uncertainty relation τFΔH≥ℏ/2 provides a general lower bound to the characteristic time τF=ΔF/|d〈F〉/dt| with which the mean value of a generic quantum observable F can change with respect to the width ΔF of its uncertainty distribution (square root of F fluctuations). A useful practical consequence is that in unitary dynamics the states with longer lifetimes are those with smaller energy uncertainty ΔH (square root of energy fluctuations). Here we show that when unitary evolution is complemented with a steepest-entropy-ascent model of dissipation, the resulting nonlinear master equation entails that these lower bounds get modified and depend also on the entropy uncertainty ΔS (square root of entropy fluctuations). For example, we obtain the time–energy-and–time–entropy uncertainty relation (2τFΔH/ℏ)2+(τFΔS/kBτ)2≥1 where τ is a characteristic dissipation time functional that for each given state defines the strength of the nonunitary, steepest-entropy-ascent part of the assumed master equation. For purely dissipative dynamics this reduces to the time–entropy uncertainty relation τFΔS≥kBτ, meaning that the nonequilibrium dissipative states with longer lifetime are those with smaller entropy uncertainty ΔS.

Towards a General Definition of Life

A new definition of life is proposed and discussed in the present article. It is formulated by modifying and extending NASA's working definition of life, which postulates that life is a "self-sustaining chemical system capable of Darwinian evolution". The new definition includes a thermodynamical aspect of life as a far from equilibrium system and considers the flow of information from the environment to the living system. In our derivation of the definition of life we have assumed the hypothesis, that during the emergence of life evolution had to first involve autocatalytic systems that only subsequently acquired the capacity of genetic heredity. The new proposed definition of life is independent of the mode of evolution, regardless of whether Lamarckian or Darwinian evolution operated at the origins of life and throughout evolutionary history. The new definition of life presented herein is formulated in a minimal manner and it is general enough that it does not distinguish between individual (metabolic) network and the collective (ecological) one. The newly proposed definition of life may be of interest for astrobiology, research into the origins of life or for efforts to produce synthetic or artificial life, and it furthermore may also have implications in the cognitive and computer sciences.

Flux and storage of energy in nonequilibrium stationary states

Systems kept out of equilibrium in stationary states by an external source of energy store an energy ΔU=U-U_{0}. U_{0} is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine ΔU for two model systems: ideal gas and a Lennard-Jones fluid. ΔU depends not only on the total energy flux, J_{U}, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where the energy flux per unit volume is (i) constant, (ii) proportional to the local temperature, and (iii) proportional to the local density. We show that ΔU/J_{U}=τ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. τ is the characteristic timescale of energy outflow from the system immediately after the shutdown of energy flux. We prove that τ is minimized in stable states of the Rayleigh-Benard cell.

From an Entropic Measure of Time to Laws of Motion

A hypothesis proposed in the paper Entropy (Martyushev, L.M. Entropy2017, 19, 345) on the deductive formulation of a physical theory based on explicitly- and universally-introduced basic concepts is further developed. An entropic measure of time with a number of properties leading to an analog of the Galileo–Einstein relativity principle is considered. Using this measure and a simple model, a kinematic law which relates time to the size and number of particles of a system is obtained. Corollaries of this law are examined. In particular, accelerated growth of the system size is obtained, whereas in systems with constant size, a decrease in the number of particles is observed. An interesting corollary is the emergence of repulsive and attractive forces inversely proportional to the square of the system size for relatively dense systems and constant for systems with sufficiently low density.

Symmetry, Entropy, Diversity and (Why Not?) Quantum Statistics in Society

We describe society as an out-of-equilibrium probabilistic system: in it, N individuals occupy W resource states and produce entropy S over definite time periods. The resulting thermodynamics are however unusual, because a second entropy, H, measures inequality or diversity―a typically social feature―in the distribution of available resources. A symmetry phase transition takes place at Gini values 1/3, where realistic distributions become asymmetric. Four constraints act on S: N and W, and new ones, diversity and interactions between individuals; the latter are determined by the coordinates of a single point in the data, the peak. The occupation number of a job is either zero or one, suggesting Fermi–Dirac statistics for employment. Contrariwise, an indefinite number of individuals can occupy a state defined as a quantile of income or of age, so Bose–Einstein statistics may be required. Indistinguishability rather than anonymity of individuals and resources is thus needed. Interactions between individuals define classes of equivalence that happen to coincide with acceptable definitions of social classes or periods in human life. The entropy S is non-extensive and obtainable from data. Theoretical laws are compared to empirical data in four different cases of economic or physiological diversity. Acceptable fits are found for all of them.

A Brief Review of Generalized Entropies

Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon–Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances.

From Multiscale to Mesoscience: Addressing Mesoscales in Mesoregimes of Different Levels

This review covers three decades of research on mesoscale phenomena in chemical engineering, from the energy minimization multiscale (EMMS) model specific for gas-solid fluidization to a general principle of compromise in competition between dominant mechanisms, leading to the proposed concept of mesoscience. First, the concept of mesoscales is reviewed with respect to their commonality, diversity, and misunderstanding in different fields. Then, the evolution from the EMMS model to the EMMS principle common to all mesoscales is described to show the rationale of mesoscience referring to both mesoscales and mesoregimes. Finally, the potential universality of mesoscience and its importance, particularly to enable virtual process engineering (VPE) by realizing the consistency of logic and structure between the problem, the model, the software, and the computer, are discussed. The review concludes by illustrating possible case studies to collect more evidence and a potential framework for mesoscience.

Photosystem I, when excited in the chlorophyll Qy absorption band, feeds on negative entropy

It is often suggested that Life may lay outside the normal laws of Physics and particularly of Thermodynamics, though this point of view is refuted by many. As the Living State may be thought of as an open system, often far from equilibrium, most attempts at placing Life under the umbrella of the laws of Physics have been based, particularly in recent years, on non-equilibrium Thermodynamics and particularly the Maximum Entropy Production Principle. In this view it is the dissipation of entropy (heat) which permits the ever increasing complexity of Living Systems in biological evolution and the maintenance of this complexity. However, these studies usually consider such biological entities as whole cells, organs, whole organisms and even Life itself at the entire terrestrial level. This requires making assumptions concerning the Living State, which are often not soundly based on observation and lack a defined model structure. The present study is based on an entirely different approach, in which a classical thermodynamic analysis of a well-defined biological nanoparticle, plant Photosystem I, is performed. This photosynthetic structure, which absorbs light and performs primary and secondary charge separation, operates with a quantum efficiency close to one. It is demonstrated that when monochromatic light is absorbed by the lowest lying electronic transition, the chlorophyll Q_y transition, entropy production in the system bath plus entropy changes internal to the system are numerically less than the entropy decrease of the light field. A Second Law violation is therefore suggested for these experimental conditions. This conclusion, while at first sight is supportive of the famous and much discussed statement of Schroedinger, that "Life feeds on negentropy", is analysed and the conditions in which this statement may be considered valid for a Plant Photosystem are defined and delimited. The remarkably high quantum efficiency, leading to minimal entropy production (energy wastage), seems to suggest that evolution of Photosystem I has gone down the road of maximal energy efficiency as distinct from maximal entropy production. Photosystem I cannot be considered a maximum entropy dissipation structure.

Energy conservation and maximal entropy production in enzyme reactions

A procedure for maximization of the density of entropy production in a single stationary two-step enzyme reaction is developed. Under the constraints of mass conservation, fixed equilibrium constant of a reaction and fixed products of forward and backward enzyme rate constants the existence of maximum in the density of entropy production is demonstrated. In the state with maximal density of entropy production the optimal enzyme rate constants, the stationary concentrations of the substrate and the product, the stationary product yield as well as the stationary reaction flux are calculated. The test, whether these calculated values of the reaction parameters are consistent with their corresponding measured values, is performed for the enzyme Glucose Isomerase. It is found that calculated and measured rate constants agree within an order of magnitude, whereas the calculated reaction flux and the product yield differ from their corresponding measured values for less than 20 % and 5 %, respectively. This indicates that the enzyme Glucose Isomerase, considered in a non-equilibrium stationary state, as found in experiments using the continuous stirred tank reactors, possibly operates close to the state with the maximum in the density of entropy production.

Is the catalytic activity of triosephosphate isomerase fully optimized? An investigation based on maximization of entropy production

Triosephosphate isomerase (TIM) is often described as a fully evolved housekeeping enzyme with near-maximal possible reaction rate. The assumption that an enzyme is perfectly evolved has not been easy to confirm or refute. In this paper, we use maximization of entropy production within known constraints to examine this assumption by calculating steady-state cyclic flux, corresponding entropy production, and catalytic activity in a reversible four-state scheme of TIM functional states. The maximal entropy production (MaxEP) requirement for any of the first three transitions between TIM functional states leads to decreased total entropy production. Only the MaxEP requirement for the product (R-glyceraldehyde-3-phosphate) release step led to a 30% increase in enzyme activity, specificity constant kcat/KM, and overall entropy production. The product release step, due to the TIM molecular machine working in the physiological direction of glycolysis, has not been identified before as the rate-limiting step by using irreversible thermodynamics. Together with structural studies, our results open the possibility for finding amino acid substitutions leading to an increased frequency of loop six opening and product release.