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A Sourcebook for the Worldwide Discovery of a Creative Organic Universe
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III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet, Incubator Lifescape

D. Non-Equilibrium Thermodynamics of Living Systems

Gell-Mann, Murray and Constantino Tsallis, eds. Nonextensive Entropy – Interdisciplinary Applications. Oxford: Oxford University Press, 2004. Proceedings from an April 2002, Santa Fe Institute conference discuss how the non-equilibrium thermodynamic theories of the Greek-Brazilian physicist Constantino Tsallis apply to living systems everywhere from genomes to societies to galaxies. The intent is to move beyond 19th century Boltzman-Gibbs equilibrium statistics to a 21st century version to express nature’s universal scale-free, self-organized criticality. But as Buiatti above reflects, a ‘non-‘ terminology is used since life seems alien to the reigning mechanical model. “Nonextensive” is a term to distinguish nonlinear systems of emergent, creative complexity from the predictability of linear cause and effect. The posting by Graham next is a good introduction to the subject. A popular article on Tsallis' novel insights is "Breakout" by Mark Buchanan in the New Scientist for August 27, 2005.

The nonextensive alternative is proposed, instead, as a way of dealing, through mathematical methods that are quite similar to the usual ones, with anomalous systems. (xiv)

Gour, Gilad, et al. The Resource Theory of Informational Nonequilibrium in Thermodynamics. Physics Reports. Online May, 2015. Some two centuries since Sadi Carnot, Ludwig Boltzman, and many others, in this era of global collaboration, scientists with postings at the University of Calgary, Perimeter Institute, and elsewhere, including Markus Muller, continue the project to comprehend nature’s substantial, evolutionary, programmatic reality.

We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that they can implement for free are those that are thermal at some fixed temperature. This body of work also demonstrates that the standard formulation of the second law of thermodynamics is inadequate as a criterion for deciding whether or not a given state transition is possible. (Abstract excerpts)

Graham, Rex. Constantino Tsallis: Describing a New Entropy. www.santafe.edu/publications/bulletin/fall00/tsallis/.php. An introduction the person and his thermodynamic theories of a self-similar, temporally developing, open universe.

Grossing, Gerhard. Time’s Arrow: Irreversibility from Quantum Systems to Biological Evolution. Cybernetics and Systems. 32/3-4, 2001. An introduction to a special issue whose papers variously affirm a stratified developmental ascent toward conscious complexity.

Haddad, Wassim. A Dynamical Systems Theory of Thermodynamics. Princeton: Princeton University Press, 2019. The Georgia Tech engineering professor (search here and his website) continues into the 21st century to advance the field of scientific articulations for nature’s generative energies and forces.

This book merges thermodynamics and dynamical systems theory into a single compendium, with the latter providing an ideal language for the former, so to develop a new dynamical thermodynamics. This combined format expresses the key aspects and laws of thermodynamics so to provide a mathematical basis for systems out of equilibrium. Topics include nonequilibrium thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, critical phenomena with phase transitions, information theory, along with stochastic thermodynamics. In this way the book joins thermodynamic irreversibility, the second law, and the arrow of time to unify discreteness and continuity, indeterminism and determinism, quantum mechanics and general relativity.

Haddad, Wassim. A Unification between Dynamical System Theory and Thermodynamics Involving an Energy, Mass, and Entropy State Space Formalism. Entropy. Online May, 2013. The Georgia Institute of Technology professor of aerospace engineering and textbook author provides an innovative synthesis of these earlier and later, separate but similar, scientific interpretations. One of his courses is “Dissipative Dynamical Systems and System Thermodynamics.” In regard, humankind’s composite inquiry, its collaborative retrospect, is surely trying to describe one whole natural genesis universe through all these versions and vernaculars.

In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model involving heat flow, work energy, and chemical reactions, we develop a state-space dynamical system model that captures the key aspects of thermodynamics, including its fundamental laws. In addition, we show that our thermodynamically consistent dynamical system model is globally semistable with system states converging to a state of temperature equipartition. Furthermore, in the presence of chemical reactions, we use the law of mass-action and the notion of chemical potential to show that the dynamic system states converge to a state of temperature equipartition and zero affinity corresponding to a state of chemical equilibrium. (Abstract)

The central thesis of this paper is to present a state space formulation for equilibrium and nonequilibrium thermodynamics based on a dynamical system theory combined with interconnected nonlinear compartmental systems that ensures a consistent thermodynamic model for heat, energy, and mass flow. In particular, the proposed approach extends the framework developed in my Thermodynamics: A Dynamics Systems Approach (2005) addressing closed thermodynamic systems that exchange energy but not matter with the environment to open thermodynamic systems that exchange matter and energy with their environment. In addition, our results ….develop rigorous notions of enthalpy, Gibbs free energy, Helmholtz free energy, and Gibbs’ chemical potential using a state space formulation of dynamics, energy and mass conservation principles, as well as the law of mass-action kinetics and the law of superposition of elementary reactions without invoking statistical mechanics arguments. (1823)

The underlying intention of this paper has been to present one of the most useful and general physical branches of science in the language of dynamical systems theory. In particular, our goal has been to develop a dynamical system formalism of thermodynamics using a large-scale interconnected systems theory that bridges the gap between classical and statistical thermodynamics. The laws of thermodynamics are among the most firmly established laws of nature, and it is hoped that this work will help to stimulate increased interaction between physicists and dynamical systems and control theorists. Besides the fact that irreversible thermodynamics plays a critical role in the understanding of our physical universe, it forms the underpinning of several fundamental life science and engineering disciplines, including biological systems, physiological systems, neuroscience, chemical reaction systems, ecological systems, demographic systems, transportation systems, network systems, and power systems, to cite but a few examples. (1841-1842)

Haken, Hermann and Juval Portugali. Information and Selforganization: A Unifying Approach and Applications. Entropy. 18/6, 2016. The octogenarian University of Stuttgart physicist and 1980s founder of synergetics theory, and the Tel Aviv University systems geographer (search each) provide a tutorial upon nature’s nonlinear complexities. The authors are editors for a special collection about the title phrase, see the second quote. One may distill a common, implied theme from the technical essay, as current works evince, of an independent, universally applicable, mathematical source, which is then exemplified in kind at each stage and instance. Another typical paper in this online topic is Entropy and the Self-Organization of Information and Value by Rainer Feistel and Werner Ebeling.

Selforganization is a process by which the interaction between the parts of a complex system gives rise to the spontaneous emergence of patterns, structures or functions. In this interaction the system elements exchange matter, energy and information. We focus our attention on the relations between selforganization and information in general and the way they are linked to cognitive processes in particular. We do so from the analytical and mathematical perspective of the “second foundation of synergetics” and its “synergetic computer” and with reference to several forms of information: 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. We first elucidate the relations between selforganization and information theoretically and mathematically and then by means of specific case studies. (Abstract)

The process of “self-organization” invokes a property that is far from equilibrium, and refers to open and complex systems that acquire spatio-temporal or functional structures without specific ordering instructions from the outside. In domains such as physics, chemistry or biology, the phrase, “far from equilibrium,” refers to systems that are “far from thermal equilibrium,” while in other disciplines, the term refers to the property of being “away from the resting state.” Such systems are “complex” in the sense that they are composed of many interacting components, parts, elements, etc., and “open” in the sense that they exchange with their environment matter, energy, and information. This Special Issue aims to deal with the different ways processes of self-organization are linked with the various forms of information. A prominent example is the concept of information adaptation, whereby Shannon information and semantic information condition each other. A study of such links has consequences on a number of research domains, ranging from physics and chemistry, through the life sciences and cognitive science, including human behavior and action, to our understanding of society, economics, and the dynamics of cities and urbanization. (Special Issue Summary)

Haw, Mark. The Industry of Life. Physics World. November, 2007. On the occasion of the 100 year anniversary of the death of William Thomson, aka Lord Kelvin, a retrospective history of thermodynamic theories of energy transmission and use which he played a major role in. But as this first phase of the three laws is complete, the subject has now moved to a non-equilibrium expression of living systems as a “theory of what everything does.”

Hernando, Alberto and Angel Plastino. The Thermodynamics of Urban Population Flows. Physical Review E. 86/066105, 2012. As a natural genesis from universe to human becomes appreciated as a single, invariantly recurrent, procreative process, Universite Paul Sabitier, Toulouse, and National University La Plata, Argentina, physicists proceed to quantify from cosmos to cities a self-similar, iterative structure and dynamics as every other scale in between. In regard, by analogy, a “social thermodynamics” is then broached. See also in arXiv their paper “Space-Time Correlations in Urban Population Flows.”

The application of mathematical models to social sciences has a long and distinguished history. One may speak of empirical data from scientific collaboration networks, cites of physics journals, the Internet traffic, Linux packages links, popularity of chess openings, as well as electoral results, urban agglomerations and firm sizes all over the world. A specially relevant issue is that of universality classes defined by to the so-called Zipf’s law ZL in the cumulative distribution or rank- size distributions. The class emerges from a condition of dynamic equilibrium. ZL also applies for processes involving either self-similarity or fractal hierarchy, all of them mere examples amongst very general stochastic ones. In the present vein, still another kind of idiosyncratic distribution is often reported: the log-normal one, that has been observed in biology (length and sizes of living tissue), finance, and firm sizes. Together with geometric Brownian motion, there is a variety of models arising in different fields that yield Zipf’s law and other power laws on a case-by-case basis, as preferential attachment and competitive cluster growth in complex networks, used to explain many of the scale-free properties of social networks. Of course, the renormalization group is intimately related to scale invariance and associated techniques have been fruitfully exploited in these Matters. We will here describe the manner in which the methods of that paper can be generalized to first-principles theoretical framework describing population flows in terms of thermodynamic concepts. (066105-1)

Hu, Bei-Lok. Emergence, Gravity and Thermodynamics. arXiv:1204.1077. This is a full posting of a presentation by the University of Maryland and Hong Kong University physicist at the 2011 Heinz von Foerster Centenary International Conference on Self-Organization and Emergence in Vienna (Google). We cite this work as another example of joining these title aspects within a 2010s quantum revolution, by our composite humankind, which seems on its own way to finally sorting out, clarifying, unifying a viable scenario of a self-discovering and self-creating genesis.

Emergence: After describing three different senses of emergence, I point out that effective field theory (EFT) or renormalization group (RG) is a suitable, maybe even necessary, but not sufficient set of conceptual means for describing emergence. EFT or RG [A1] may suggest how different physics manifest at different scales, but one also needs to identify the mechanisms or processes whereby different levels of structures and the laws governing them, including the symmetry principles, emerge. That depends on deeper interplay of collectivity, complexity, stochasticity and self-organization. Emergent Gravity: There are at least two intimately related veins in viewing gravity as emergent: a) General Relativity as Hydrodynamics, b) Gravity as Thermodynamics , where such a view is often shaped by considering the effects of an event horizon on the quantum fluctuations of a field, which underlies what is known today as the holography principle.

Gravity and Thermodynamics: Since both gravity and thermodynamics are classical theories of macroscopic structures, if a deep connection exists, we should be able to see their direct relation at this level, without relying on arguments invoking the microscopic structure of matter (quantum fluctuations). If we can meet this challenge we may see the simpler and deeper connection between gravity and thermodynamics without invoking quantum mechanics. If we fail we will perhaps see more clearly the essential role of quantum physics in explaining gravity and the necessary implication that a) either the macroscopic world is fundamentally quantum, b) quantum mechanics is also emergent from a deeper structure, a representation of stochastic processes, or as a form of organizational rules like statistical mechanics. (Abstract excerpts)

Ito, Sosuke. Unified Framework for the Second Law of Thermodynamics and Information Thermodynamics based on Information Geometry. arXiv:1810.09545. A Hokkaido University, Research Center of Mathematics for Social Creativity continues his project with colleagues to advance a synthesis of dynamic energies and an operational, prescriptive content. See also Stochastic Thermodynamic Interpretation of Information Geometry by SI at 1712.04311 (second abstract).

Information geometry, which is a differential geometric method of information theory, gives a natural definition of informational quantity from the projection theorem. We report that the second law of thermodynamics can be obtained from this projection onto the manifold of reversible dynamics. We also show that the recent result in stochastic thermodynamics with information theory, called as the second law of information thermodynamics. The hierarchy of these second laws can be discussed in terms of inclusion property of manifolds. (1810.09545 Abstract)

In recent years, the unified theory of information and thermodynamics has been discussed in the context of stochastic thermodynamics. The unified theory reveals that information theory would be useful to understand non-stationary dynamics of systems far from equilibrium. In this letter, we have found a new link between stochastic thermodynamics and information theory well known as information geometry. By applying this link, an information geometric inequality can be interpreted as a thermodynamic uncertainty relationship between speed and thermodynamic cost. (1712.04311 Abstract)

Iyer-Biswas, Srividya, et al. Universality in Stochastic Exponential Growth. arXiv:1407.2947. We note this entry by University of Chicago and LBNL theorists including Gavin Crooks to report upon mid 2010s thermodynamic frontiers, broadly conceived, along with an increased notice of universally recurrent autocatalysis.

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth. (Abstract excerpt)

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