Functional Interdependence in Coupled Dissipative Structures: Physical Foundations of Biological Coordination

Coordination within and between organisms is one of the most complex abilities of living systems, requiring the concerted regulation of many physiological constituents, and this complexity can be particularly difficult to explain by appealing to physics. A valuable framework for understanding biological coordination is the coordinative structure, a self-organized assembly of physiological elements that collectively performs a specific function. Coordinative structures are characterized by three properties: (1) multiple coupled components, (2) soft-assembly, and (3) functional organization. Coordinative structures have been hypothesized to be specific instantiations of dissipative structures, non-equilibrium, self-organized, physical systems exhibiting complex pattern formation in structure and behaviors. We pursued this hypothesis by testing for these three properties of coordinative structures in an electrically-driven dissipative structure. Our system demonstrates dynamic reorganization in response to functional perturbation, a behavior of coordinative structures called reciprocal compensation. Reciprocal compensation is corroborated by a dynamical systems model of the underlying physics. This coordinated activity of the system appears to derive from the system’s intrinsic end-directed behavior to maximize the rate of entropy production. The paper includes three primary components: (1) empirical data on emergent coordinated phenomena in a physical system, (2) computational simulations of this physical system, and (3) theoretical evaluation of the empirical and simulated results in the context of physics and the life sciences. This study reveals similarities between an electrically-driven dissipative structure that exhibits end-directed behavior and the goal-oriented behaviors of more complex living systems.     

Statistical-Mechanical Foundations for a Generalized Thermodynamics of Dissipative Processes

A statistical-mechanical formalism for nonequilibrium systems, namely the nonequilibrium statistical operator method, provides microscopic foundations for a generalized thermodynamics of dissipative processes. This formalism is based on a unifying variational approach that is considered to be encompassed in Jaynes' Predictive Statistical Mechanics and principle of maximization of the statistical-informational entropy. Within the framework of the statistical thermodynamics that follows from the method, we demonstrate the existence of generalized forms of the theorem of minimum (informational) entropy production, the criterion for evolution, and the thermodynamic (in)stability criterion. The formalism is not restricted to local equilibrium but, in principle, to general conditions (its complete domain of validity is not yet fully determined). A H-theorem associated to the formalism is presented in the form of an increase of the informational entropy along the evolution of the system. Some of the results are illustrated in an application to the study of a model for a photoexcited direct-gap semiconductor.     

论动态信息理论

本文综述了作者的研究成果.近十年,作者将现有静态统计信息理论拓展至动态过程,建立了以表述动态信息演化规律的动态信息演化方程为核心的动态统计信息理论.基于服从随机性规律的动力学系统(如随机动力学系统和非平衡态统计物理系统)与遵守确定性规律的动力学系统(如电动力学系统)的态变量概率密度演化方程都可看成是其信息符号演化方程,推导出了动态信息(熵)演化方程.它们表明:对于服从随机性规律的动力学系统,动态信息密度随时间的变化率是由其在系统内部的态变量空间和传递过程的坐标空间的漂移、扩散和耗损三者引起的,而动态信息熵密度随时间的变化率则是由其在系统内部的态变量空间和传递过程的坐标空间的漂移、扩散和产生三者引起的.对于遵守确定性规律的动力学系统,动态信息(熵)演化方程与前者的相比,除动态信息(熵)密度在系统内部的态变量空间仅有漂移外,其余皆相同.信息和熵已与系统的状态和变化规律结合在一起,信息扩散和信息耗损同时存在.当空间噪声可略去时,将会出现信息波.若仅研究系统内部的信息变化,动态信息演化方程就约化为与表述上述动力学系统变化规律的动力学方程相对应的信息方程,它既可看成是表述动力学系统动态信息的演化规律,亦可看成是动力学系统的变化规律都可由信息方程表述.进而给出了漂移和扩散信息流公式、信息耗散率公式和信息熵产生率公式及动力学系统退化和进化的统一信息表述公式.得到了反映信息在传递过程中耗散特性的动态互信息公式和动态信道容量公式,它们在信道长度和信号传递速度之比趋于零的极限情况下变为现有的静态互信息公式和静态信道容量公式.所有这些新的理论公式和结果都是从动态信息演化方程统一推导出的.     

Entropy balance in distributed reversible Gray-Scott model

A practical way to calculate the entropy change in the distributed media composed of reversible Gray-Scott model is demonstrated. The entropy change is given as the sum of the entropy production and the divergence of entropy flow. The divergence of entropy is calculated based on the chemical potential of steady state. It becomes evident that: (i) the entropy change for the emergence of dissipative structures in the open system can be positive or negative, (ii) most of the entropy produced inside the system is thrown out to the environment when dissipative structures are developing, (iii) the entropy production and the divergence of entropy flow balance completely, when the system shows static steady states, (iv) the entropy change behaves as if it is the time derivative of the entropy production. Prior to these calculations of entropy balance, the features of emergent patterns in the two-dimensional system are examined in terms of entropy production solely. The results imply that the entropy production can be an index for us to discriminate spatial patterns, but is not a global thermodynamic potential for the evolution of dissipative structures.     

Dynamic information theory and information description of dynamic systems

In this paper, we develop dynamic statistical information theory established by the author. Starting from the ideas that the state variable evolution equations of stochastic dynamic systems, classical and quantum nonequilibrium statistical physical systems and special electromagnetic field systems can be regarded as their information symbol evolution equations and the definitions of dynamic information and dynamic entropy, we derive the evolution equations of dynamic information and dynamic entropy that des...     

A Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks

Dissipative accounts of structure formation show that the self-organisation of complex structures is thermodynamically favoured, whenever these structures dissipate free energy that could not be accessed otherwise. These structures therefore open transition channels for the state of the universe to move from a frustrated, metastable state to another metastable state of higher entropy. However, these accounts apply as well to relatively simple, dissipative systems, such as convection cells, hurricanes, candle flames, lightning strikes, or mechanical cracks, as they do to complex biological systems. Conversely, interesting computational properties—that characterize complex biological systems, such as efficient, predictive representations of environmental dynamics—can be linked to the thermodynamic efficiency of underlying physical processes. However, the potential mechanisms that underwrite the selection of dissipative structures with thermodynamically efficient subprocesses is not completely understood. We address these mechanisms by explaining how bifurcation-based, work-harvesting processes—required to sustain complex dissipative structures—might be driven towards thermodynamic efficiency. We first demonstrate a simple mechanism that leads to self-selection of efficient dissipative structures in a stochastic chemical reaction network, when the dissipated driving chemical potential difference is decreased. We then discuss how such a drive can emerge naturally in a hierarchy of self-similar dissipative structures, each feeding on the dissipative structures of a previous level, when moving away from the initial, driving disequilibrium.     

Dynamical ensembles in stationary states

We propose, as a generalization of an idea of Ruelle's to describe turbulent fluid flow, a chaotic hypothesis for reversible dissipative many-particle systems in nonequilibrium stationary states in general. This implies an extension of the zeroth law of thermodynamics to nonequilibrium states and it leads to the identification of a unique distribution describing the asymptotic properties of the time evolution of the system for initial data randomly chosen with respect to a uniform distribution on phase space. For conservative systems in thermal equilibrium the chaotic hypothesis implies the ergodic hypothesis. We outline a procedure to obtain the distribution : it leads to a new unifying point of view for the phase space behavior of dissipative and conservative systems. The chaotic hypothesis is confirmed in a nontrivial, parameter-free, way by a recent computer experiment on the entropy production fluctuations in a shearing fluid far from equilibrium. Similar applications to other models are proposed, in particular to a model for the Kolmogorov-Obuchov theory for turbulent flow.     

Accumulation of Particles and Formation of a Dissipative Structure in a Nonequilibrium Bath

The standard textbooks contain good explanations of how and why equilibrium thermodynamics emerges in a reservoir with particles that are subjected to Gaussian noise. However, in systems that convert or transport energy, the noise is often not Gaussian. Instead, displacements exhibit an α-stable distribution. Such noise is commonly called Lévy noise. With such noise, we see a thermodynamics that deviates from what traditional equilibrium theory stipulates. In addition, with particles that can propel themselves, so-called active particles, we find that the rules of equilibrium thermodynamics no longer apply. No general nonequilibrium thermodynamic theory is available and understanding is often ad hoc. We study a system with overdamped particles that are subjected to Lévy noise. We pick a system with a geometry that leads to concise formulae to describe the accumulation of particles in a cavity. The nonhomogeneous distribution of particles can be seen as a dissipative structure, i.e., a lower-entropy steady state that allows for throughput of energy and concurrent production of entropy. After the mechanism that maintains nonequilibrium is switched off, the relaxation back to homogeneity represents an increase in entropy and a decrease of free energy. For our setup we can analytically connect the nonequilibrium noise and active particle behavior to entropy decrease and energy buildup with simple and intuitive formulae.     

Time Evolution in Macroscopic Systems. II. The Entropy

The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be defined unambiguously, but it is the time derivative or entropy production that governs ongoing processes in these systems. The differences in physical interpretation and thermodynamic role of entropy in equilibrium and nonequilibrium systems is emphasized and the observable aspects of entropy production are noted. A basis for nonequilibrium thermodynamics is also outlined.     

Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators

We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization.     

Spatial correlations in nonequilibrium systems: The effect of diffusion

We show how the ideas of the fluctuation-dissipation theory can be used to calculate spatial correlations in interacting systems away from equilibrium. The only spatially dependent dissipative process considered is diffusion, and spatial correlations are generated by the nonlocal spatial dependence of the chemical potential. The results are the lowest order in a hierarchy of generalized hydrodynamic type calculations applicable to nonequilibrium systems. We derive equations for the density correlation functions at stationary state supported by diffusive fluxes and show that they have the local equilibrium form. The static correlation function is obtained from the fluctuation-dissipation theorem, which we show to be equivalent to the Ornstein-Zernike integral equation. At equilibrium we demonstrate that the dynamical structure factor obtained by these methods includes the expected wave-vector dependent diffusion constant. Finally we derive a necessary and sufficient condition for local equilibrium to obtain at a stationary state and show by explicit calculation that chemical processes can give rise to significant nonequilibrium correlations.     

Symplectic Foliation Structures of Non-Equilibrium Thermodynamics as Dissipation Model: Application to Metriplectic Nonlinear Lindblad Quantum Master Equation

The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action. A novel symplectic thermodynamics and information geometry known as “Lie group thermodynamics” then explains foliation structures of thermodynamics. We then infer a geometric structure for heat equation from this archetypal model, and we have discovered a pure geometric structure of entropy, which characterizes entropy in coadjoint representation as an invariant Casimir function. The coadjoint orbits form the level sets on the entropy. By using the KKS 2-form in the affine case via Souriau’s cocycle, the method also enables the Fisher metric from information geometry for Lie groups. The fact that transverse dynamics to these symplectic leaves is dissipative, whilst dynamics along these symplectic leaves characterize non-dissipative phenomenon, can be used to interpret this Lie group thermodynamics within the context of an open system out of thermodynamics equilibrium. In the following section, we will discuss the dissipative symplectic model of heat and information through the Poisson transverse structure to the symplectic leaf of coadjoint orbits, which is based on the metriplectic bracket, which guarantees conservation of energy and non-decrease of entropy. Baptiste Coquinot recently developed a new foundation theory for dissipative brackets by taking a broad perspective from non-equilibrium thermodynamics. He did this by first considering more natural variables for building the bracket used in metriplectic flow and then by presenting a methodical approach to the development of the theory. By deriving a generic dissipative bracket from fundamental thermodynamic first principles, Baptiste Coquinot demonstrates that brackets for the dissipative part are entirely natural, just as Poisson brackets for the non-dissipative part are canonical for Hamiltonian dynamics. We shall investigate how the theory of dissipative brackets introduced by Paul Dirac for limited Hamiltonian systems relates to transverse structure. We shall investigate an alternative method to the metriplectic method based on Michel Saint Germain’s PhD research on the transverse Poisson structure. We will examine an alternative method to the metriplectic method based on the transverse Poisson structure, which Michel Saint-Germain studied for his PhD and was motivated by the key works of Fokko du Cloux. In continuation of Saint-Germain’s works, Hervé Sabourin highlights the, for transverse Poisson structures, polynomial nature to nilpotent adjoint orbits and demonstrated that the Casimir functions of the transverse Poisson structure that result from restriction to the Lie–Poisson structure transverse slice are Casimir functions independent of the transverse Poisson structure. He also demonstrated that, on the transverse slice, two polynomial Poisson structures to the symplectic leaf appear that have Casimir functions. The dissipative equation introduced by Lindblad, from the Hamiltonian Liouville equation operating on the quantum density matrix, will be applied to illustrate these previous models. For the Lindblad operator, the dissipative component has been described as the relative entropy gradient and the maximum entropy principle by Öttinger. It has been observed then that the Lindblad equation is a linear approximation of the metriplectic equation.     

Nonequilibrium Thermodynamics of Polymeric Liquids via Atomistic Simulation

The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption of an evolution of quasie equilibrium states in which the requisite internal variables relax on different time scales. The nonequilibrium entropy can be determined at various levels of coarse-graining of the polymer chains by statistical expressions involving nonequilibrium distribution functions that depend on the type of flow and the flow strength. Using nonequilibrium molecular dynamics simulations of a linear, monodisperse, entangled C₁₀₀₀H₂₀₀₂ polyethylene melt, nonequilibrium entropy was calculated directly from the nonequilibrium distribution functions, as well as from their second moments, and also using the radial distribution function at various levels of coarse-graining of the constituent macromolecular chains. Surprisingly, all these different methods of calculating the nonequilibrium entropy provide consistent values under both planar Couette and planar elongational flows. Combining the nonequilibrium entropy with the internal energy allows determination of the Helmholtz free energy, which is used as a generating function of flow dynamics in nonequilibrium thermodynamic theory.     

Thermodynamics of Currents in Nonequilibrium Diffusive Systems: Theory and Simulation

Understanding the physics of nonequilibrium systems remains as one of the major challenges of modern theoretical physics. We believe nowadays that this problem can be cracked in part by investigating the macroscopic fluctuations of the currents characterizing nonequilibrium behavior, their statistics, associated structures and microscopic origin. This fundamental line of research has been severely hampered by the overwhelming complexity of this problem. However, during the last years two new powerful and general methods have appeared to investigate fluctuating behavior that are changing radically our understanding of nonequilibrium physics: a powerful macroscopic fluctuation theory (MFT) and a set of advanced computational techniques to measure rare events. In this work we study the statistics of current fluctuations in nonequilibrium diffusive systems, using macroscopic fluctuation theory as theoretical framework, and advanced Monte Carlo simulations of several stochastic lattice gases as a laboratory to test the emerging picture. Our quest will bring us from (1) the confirmation of an additivity conjecture in one and two dimensions, which considerably simplifies the MFT complex variational problem to compute the thermodynamics of currents, to (2) the discovery of novel isometric fluctuation relations, which opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations, and to (3) the observation of coherent structures in fluctuations, which appear via dynamic phase transitions involving a spontaneous symmetry breaking event at the fluctuating level. The clear-cut observation, measurement and characterization of these unexpected phenomena, well described by MFT, strongly support this theoretical scheme as the natural theory to understand the thermodynamics of currents in nonequilibrium diffusive media, opening new avenues of research in nonequilibrium physics.     

On the formation of dissipative spatial patterns of charge carriers in biosystems

Summary It is shown that in systems like large aggregates of biological molecules, population inversion of charge carriers, for example as produced by photoexcitation processes, may have competitive advantage beyond critical levels of excitation to produce ordered spatial structures (morphological transitions). In our analysis electromagnetic radiation transfers electrons from bonding states into a continuum of itinerant antibonding states in ap-type doped sample. In this system, in which energy is pumped continuously by an external source, the interplay of collective and dissipative processes can be responsible for the condensation of a self-organized spatially ordered structure. The study we present here is carried out resorting to the powerful nonequilibrium statistical operator method, thus showing that it can be provide a mechano-statistical formalism at the microscopic level for the treatment of Prigogine's synergetic dissipative structures. The authors of this paper have agreed to not receive the proofs for correction     

Life,gravity and the second law of thermodynamics

We review the cosmic evolution of entropy and the gravitational origin of the free energy required by life. All dissipative structures in the universe including all forms of life, owe their existence to the fact that the universe started in a low entropy state and has not yet reached equilibrium. The low initial entropy was due to the low gravitational entropy of the nearly homogeneously distributed matter and has, through gravitational collapse, evolved gradients in density, temperature, pressure and chemistry. These gradients, when steep enough, give rise to far from equilibrium dissipative structures (e.g., galaxies, stars, black holes, hurricanes and life) which emerge spontaneously to hasten the destruction of the gradients which spawned them. This represents a paradigm shift from “we eat food” to “food has produced us to eat it”.     

Destructive effects of the artificial control of substances on fluctuations in dissipative structures of chemically reactive systems

We investigate the fluctuations of concentrations inherent in unimolecular reaction systems. Even when the concentration of a substance is well controlled, we find inevitable fluctuations of the concentration, which affect destructively the dissipative structures in nonequilibrium maintained by the unimolecular reaction.     

Influence of Coulomb Interactions on Dissipative Structures in Reaction-Diffusion Systems

Reaction-Diffusion-Systems with charged particles are considered. Conditions for the appearance of dissipative structures because of disturbances of an uniform initial stationary state in continuous and simple compartment systems are derived. As an example the appearance of a dissipative structure is demonstrated in a simple capacitor model. Based on this effect nonequilibrium electrical cells could be developed.     

Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems

For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. 145:1275, 2011). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.