Natural hierarchy emerges from energy dispersal

Hierarchical network structure as the source of hierarchical dynamics (power-law frequency spectra) in living and non-living systems: How state-trait continua (body plans, personalities) emerge from first principles in biophysics

Living systems are hierarchical control systems that display a small world network structure. In such structures, many smaller clusters are nested within fewer larger ones, producing a fractal-like structure with a 'power-law' cluster size distribution (a mereology). Just like their structure, the dynamics of living systems shows fractal-like qualities: the timeseries of inner message passing and overt behavior contain high frequencies or 'states' (treble) that are nested within lower frequencies or 'traits' (bass), producing a power-law frequency spectrum that is known as a 'state-trait continuum' in the behavioral sciences. Here, we argue that the power-law dynamics of living systems results from their power-law network structure: organisms 'vertically encode' the deep spatiotemporal structure of their (anticipated) environments, to the effect that many small clusters near the base of the hierarchy produce high frequency signal changes and fewer larger clusters at its top produce ultra-low frequencies. Such ultra-low frequencies exert a tonic regulatory pressure that produces morphological as well as behavioral traits (i.e., body plans and personalities). Nested-modular structure causes higher frequencies to be embedded within lower frequencies, producing a power-law state-trait continuum. At the heart of such dynamics lies the need for efficient energy dissipation through networks of coupled oscillators, which also governs the dynamics of non-living systems (e.q., earthquakes, stock market fluctuations). Since hierarchical structure produces hierarchical dynamics, the development and collapse of hierarchical structure (e.g., during maturation and disease) should leave specific traces in system dynamics (shifts in lower frequencies, i.e. morphological and behavioral traits) that may serve as early warning signs to system failure. The applications of this idea range from (bio)physics and phylogenesis to ontogenesis and clinical medicine.

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.

Is information the other face of causation in biological systems?

Is information the other face of causation? This issue cannot be clarified without discussing how these both are related to physical laws, logic, computation, networks, bio-signaling, and the mind-body problem. The relation between information and causation is also intrinsically linked to many other concepts in complex systems theory such as emergence, self-organization, synergy, criticality, and hierarchy, which in turn involve various notions such as observer-dependence, dimensionality reduction, and especially downward causation. A canonical example proposed for downward causation is the collective behavior of the whole system at a macroscale that may affect the behavior of each its member at a microscale. In neuroscience, downward causation is suggested as a strong candidate to account for mental causation (free will). However, this would be possible only on the condition that information might have causal power. After introducing the Causal Equivalence Principle expanding the relativity principle for coarse-grained and fine-grained linear causal chains, and a set-theoretical definition of multiscale nested hierarchy composed of modular ⊂-chains, it is shown that downward causation can be spurious. It emerges only in the eyes of an observer, though, due to information that could not be obtained by "looking" exclusively at the behavior of a system at a microscale. On the other hand, since biological systems are hierarchically organized, this information gain is indicative of how information can be a function of scale in these systems and a prerequisite for scale-dependent emergence of cognition and consciousness in neural networks.

On the rules of life and Kleiber's law: the macroscopic relationship between materials and energy

Efforts to accommodate the growth in global energy consumption within a fragile biosphere are primarily focused on managing the transition towards a low-carbon energy mix. We show evidence that a more fundamental problem exists through a scaling relation, akin to Kleiber's Law, between society's energy consumption and material stocks. Humanity's energy consumption scales at 0.78 of its material stocks, which implies predictable environmental pressure regardless of the energy mix. If true, future global energy scenarios imply vast amounts of materials and corresponding environmental degradation, which have not been adequately acknowledged. Thus, limits to energy consumption are needed regardless of the energy mix to stabilize human intervention in the biosphere.

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.

Statistical Physics of Evolving Systems

Evolution is customarily perceived as a biological process. However, when formulated in terms of physics, evolution is understood to entail everything. Based on the axiom of everything comprising quanta of actions (e.g., quanta of light), statistical physics describes any system evolving toward thermodynamic balance with its surroundings systems. Fluxes of quanta naturally select those processes leveling out differences in energy as soon as possible. This least-time maxim results in ubiquitous patterns (i.e., power laws, approximating sigmoidal cumulative curves of skewed distributions, oscillations, and even the regularity of chaos). While the equation of evolution can be written exactly, it cannot be solved exactly. Variables are inseparable since motions consume driving forces that affect motions (and so on). Thus, evolution is inherently a non-deterministic process. Yet, the future is not all arbitrary but teleological, the final cause being the least-time free energy consumption itself. Eventually, trajectories are computable when the system has evolved into a state of balance where free energy is used up altogether.

The Matter of Time

About a century ago, in the spirit of ancient atomism, the quantum of light was renamed the photon to suggest that it is the fundamental element of everything. Since the photon carries energy in its period of time, a flux of photons inexorably embodies a flow of time. Thus, time comprises periods as a trek comprises legs. The flows of quanta naturally select optimal paths (i.e., geodesics) to level out energy differences in the least amount of time. The corresponding flow equations can be written, but they cannot be solved. Since the flows affect their driving forces, affecting the flows, and so on, the forces (i.e., causes) and changes in motions (i.e., consequences) are inseparable. Thus, the future remains unpredictable. However, it is not all arbitrary but rather bounded by free energy. Eventually, when the system has attained a stationary state where forces tally, there are no causes and no consequences. Since there are no energy differences between the system and its surroundings, the quanta only orbit on and on. Thus, time does not move forward either but circulates.

Hierarchical Structure of Generalized Thermodynamic and Informational Entropy

The present research aimed at discussing the thermodynamic and informational aspects of entropy concept to propose a unitary perspective of its definitions as an inherent property of any system in any state. The dualism and the relation between physical nature of information and the informational content of physical states of matter and phenomena play a fundamental role in the description of multi-scale systems characterized by hierarchical configurations. A method is proposed to generalize thermodynamic and informational entropy property and characterize the hierarchical structure of its canonical definition at macroscopic and microscopic levels of a system described in the domain of classical and quantum physics. The conceptual schema is based on dualisms and symmetries inherent to the geometric and kinematic configurations and interactions occurring in many-particle and few-particle thermodynamic systems. The hierarchical configuration of particles and sub-particles, representing the constitutive elements of physical systems, breaks down into levels characterized by particle masses subdivision, implying positions and velocities degrees of freedom multiplication. This hierarchy accommodates the allocation of phenomena and processes from higher to lower levels in the respect of the equipartition theorem of energy. However, the opposite and reversible process, from lower to higher level, is impossible by virtue of the Second Law, expressed as impossibility of Perpetual Motion Machine of the Second Kind (PMM2) remaining valid at all hierarchical levels, and the non-existence of Maxwell’s demon. Based on the generalized definition of entropy property, the hierarchical structure of entropy contribution and production balance, determined by degrees of freedom and constraints of systems configuration, is established. Moreover, as a consequence of the Second Law, the non-equipartition theorem of entropy is enunciated, which would be complementary to the equipartition theorem of energy derived from the First Law.

Subsumed complexity: abiogenesis as a by-product of complex energy transduction

The origins of life bring into stark relief the inadequacy of our current synthesis of thermodynamic, chemical, physical and information theory to predict the conditions under which complex, living states of organic matter can arise. Origins research has traditionally proceeded under an array of implicit or explicit guiding principles in lieu of a universal formalism for abiogenesis. Within the framework of a new guiding principle for prebiotic chemistry called subsumed complexity, organic compounds are viewed as by-products of energy transduction phenomena at different scales (subatomic, atomic, molecular and polymeric) that retain energy in the form of bonds that inhibit energy from reaching the ground state. There is evidence for an emergent level of complexity that is overlooked in most conceptualizations of abiogenesis that arises from populations of compounds formed from atomic energy input. We posit that different forms of energy input can exhibit different degrees of dissipation complexity within an identical chemical medium. By extension, the maximum capacity for organic chemical complexification across molecular and macromolecular scales subsumes, rather than emerges from, the underlying complexity of energy transduction processes that drive their production and modification.This article is part of the themed issue 'Reconceptualizing the origins of life'.

Discourse on order vs. disorder

The second law of thermodynamics is on one hand understood to account for irrevocable flow of energy from the top down, on the other hand it is seen to imply irreversible increase of disorder. This tension between the 2 stances is resolved in favor of the free energy consumption when entropy is derived from the statistical mechanics of open systems. The change in entropy is shown to map directly to the decrease in free energy without any connotation attached to disorder. Increase of disorder, just as order, is found to be merely a consequence of free energy consumption. The erroneous association of disorder with entropy stems from an unwarranted assumption that a system could undergo changes of state without concomitant dissipation, i.e., a change in energy.

The Thermodynamics of Marine Biogeochemical Cycles: Lotka Revisited

Nearly 100 years ago, Alfred Lotka published two short but insightful papers describing how ecosystems may organize. Principally, Lotka argued that ecosystems will grow in size and that their cycles will spin faster via predation and nutrient recycling so as to capture all available energy, and that evolution and natural selection are the mechanisms by which this occurs and progresses. Lotka's ideas have often been associated with the maximum power principle, but they are more consistent with recent developments in nonequilibrium thermodynamics, which assert that complex systems will organize toward maximum entropy production (MEP). In this review, we explore Lotka's hypothesis within the context of the MEP principle, as well as how this principle can be used to improve marine biogeochemistry models. We need to develop the equivalent of a climate model, as opposed to a weather model, to understand marine biogeochemistry on longer timescales, and adoption of the MEP principle can help create such models.

Living is information processing: from molecules to global systems

We extend the concept that life is an informational phenomenon, at every level of organisation, from molecules to the global ecological system. According to this thesis: (a) living is information processing, in which memory is maintained by both molecular states and ecological states as well as the more obvious nucleic acid coding; (b) this information processing has one overall function-to perpetuate itself; and (c) the processing method is filtration (cognition) of, and synthesis of, information at lower levels to appear at higher levels in complex systems (emergence). We show how information patterns, are united by the creation of mutual context, generating persistent consequences, to result in 'functional information'. This constructive process forms arbitrarily large complexes of information, the combined effects of which include the functions of life. Molecules and simple organisms have already been measured in terms of functional information content; we show how quantification may be extended to each level of organisation up to the ecological. In terms of a computer analogy, life is both the data and the program and its biochemical structure is the way the information is embodied. This idea supports the seamless integration of life at all scales with the physical universe. The innovation reported here is essentially to integrate these ideas, basing information on the 'general definition' of information, rather than simply the statistics of information, thereby explaining how functional information operates throughout life.

The significance of sex

Sexual and asexual modes of proliferation are associated with advantages and disadvantages, yet a profound percept that would account for both ways of reproduction is missing. On the basis of the 2nd law of thermodynamics we find that both sexual and asexual reproduction can be regarded as a means to consume free energy in least time. Parthenogenesis is a fast way to consume a rich repository of free energy, e.g., an ample stock of food with a large number of individuals, whereas sexual reproduction is a fast way to consume diverse and dispersed resources with a large variety of individuals. Most organisms have adapted to their surroundings accordingly and some organisms switch from one mode of reproduction to the other depending on the amount and dispersion of free-energy sources. We conclude that the least-time free energy consumption in respective surroundings, as the general criterion of natural selection, determines also sexual and asexual modes of reproduction.

The constructal law and the evolution of design in nature

The constructal law accounts for the universal phenomenon of generation and evolution of design (configuration, shape, structure, pattern, rhythm). This phenomenon is observed across the board, in animate, inanimate and human systems. The constructal law states the time direction of the evolutionary design phenomenon. It defines the concept of design evolution in physics. Along with the first and second law, the constructal law elevates thermodynamics to a science of systems with configuration. In this article we review the more recent work of our group, with emphasis on the advances made with the constructal law in the natural sciences. Highlighted are the oneness of animate and inanimate designs, the origin of finite-size organs on animals and vehicles, the flow of stresses as the generator of design in solid structures (skeletons, vegetation), the universality and rigidity of hierarchy in all flow systems, and the global design of human flows. Noteworthy is the tapestry of distributed energy systems, which balances nodes of production with networks of distribution on the landscape, and serves as key to energy sustainability and empowerment. At the global level, the constructal law accounts for the geography and design of human movement, wealth and communications.

Ecological succession as an energy dispersal process

Ecological succession is described by the 2nd law of thermodynamics. According to the universal law of the maximal energy dispersal, an ecosystem evolves toward a stationary state in its surroundings by consuming free energy via diverse mechanisms. Species are the mechanisms that conduct energy down along gradients between repositories of energy which consist of populations at various thermodynamic levels. The salient characteristics of succession, growing biomass production, increasing species richness and shifting distributions of species are found as consequences of the universal quest to diminish energy density differences in least time. The analysis reveals that during succession the ecosystem's energy transduction network, i.e., the food web organizes increasingly more effective in the free energy reduction by acquiring new, more effective and abandoning old, less effective species of energy transduction. The number of species does not necessarily peak at the climax state that corresponds to the maximum-entropy partition of species maximizing consumption of free energy. According to the theory of evolution by natural selection founded on statistical physics of open systems, ecological succession is one among many other evolutionary processes.

The physical character of information

The mathematical theory of communication defines information in syntax without reference to its physical representation and semantic significance. However, in an everyday context, information is tied to its representation and its content is valued. The dichotomy between the formal definition and the practical perception of information is examined by the second law of thermodynamics that was recently formulated as an equation of motion. Thermodynamic entropy shows that the physical representation of information is not inconsequential in generation, transmission and processing of information. According to the principle of increasing entropy, communication by dissipative transformations is a natural process among many other evolutionary phenomena that level energy-density differences between components of a communication system and its surroundings. In addition, information-guided processes direct down along descents on free energy landscapes. The non-integrable equation for irreversible processes reveals that there is no universal analytical algorithm to match source to channel. Noise infiltration is also regarded by the second law as an inevitable consequence of energy transduction between a communication system and its surroundings. Communication is invariably associated with misunderstanding because mechanisms and means of information processing at the receiver differ from those at the sender. The significance of information is ascribed to the increase in thermodynamic entropy in the receiver system that results from execution of the received message.