Nonequilibrium Thermodynamic Description Research Articles

The Non-Equilibrium Thermodynamics of Natural Selection: From Molecules to the Biosphere.

Evolutionary theory suggests that the origin, persistence, and evolution of biology is driven by the "natural selection" of characteristics improving the differential reproductive success of the organism in the given environment. The theory, however, lacks physical foundation, and, therefore, at best, can only be considered a heuristic narrative, of some utility for assimilating the biological and paleontological data at the level of the organism. On deeper analysis, it becomes apparent that this narrative is plagued with problems and paradoxes. Alternatively, non-equilibrium thermodynamic theory, derived from physical law, provides a physical foundation for describing material interaction with its environment at all scales. Here we describe a "natural thermodynamic selection" of characteristics of structures (or processes), based stochastically on increases in the global rate of dissipation of the prevailing solar spectrum. Different mechanisms of thermodynamic selection are delineated for the different biotic-abiotic levels, from the molecular level at the origin of life, up to the level of the present biosphere with non-linear coupling of biotic and abiotic processes. At the levels of the organism and the biosphere, the non-equilibrium thermodynamic description of evolution resembles, respectively, the Darwinian and Gaia descriptions, although the underlying mechanisms and the objective function of selection are fundamentally very different.

A Thermodynamically Consistent, Microscopically-Based, Model of the Rheology of Aggregating Particles Suspensions.

In this work, we outline the development of a thermodynamically consistent microscopic model for a suspension of aggregating particles under arbitrary, inertia-less deformation. As a proof-of-concept, we show how the combination of a simplified population-balance-based description of the aggregating particle microstructure along with the use of the single-generator bracket description of nonequilibrium thermodynamics, which leads naturally to the formulation of the model equations. Notable elements of the model are a lognormal distribution for the aggregate size population, a population balance-based model of the aggregation and breakup processes and a conformation tensor-based viscoelastic description of the elastic network of the particle aggregates. The resulting example model is evaluated in steady and transient shear forces and elongational flows and shown to offer predictions that are consistent with observed rheological behavior of typical systems of aggregating particles. Additionally, an expression for the total entropy production is also provided that allows one to judge the thermodynamic consistency and to evaluate the importance of the various dissipative phenomena involved in given flow processes.

Is warm inflation quasi-stable?

The present work deals with a non-equilibrium thermodynamics that is associated with the scenario of warm inflation. The premise is that an adiabatic radiation production process holds exactly i.e. the radiation dilution is exactly counterbalanced by a dissipation term. Under this hypothesis, it is found that radiation particle number, temperature, radiation energy density and pressure are all conserved – a contradiction to the very nature of the warm inflation dynamics. However, such exact adiabatic radiation production process never happens in any realistic analysis of warm inflation. In the slow roll approximation this holds at best at the zeroth order. Finally it is shown that a variable cosmological constant may accommodate the quasi-stable process in warm inflation with non-equilibrium thermodynamic description.

Mechanistic 3D finite-difference simulation of borehole spontaneous potential measurements

The quantitative interpretation of borehole spontaneous potential (SP) measurements via Nernst’s equation often relies on limiting assumptions such as shallow mud-filtrate invasion, negligible streaming potentials, and uniform borehole symmetry. To overcome these limitations while honoring the governing physics of coupled mass transport associated with SP phenomena, we have developed a 3D finite-difference algorithm to simulate borehole SP measurements acquired across water-bearing rocks that incorporates electrochemical, membrane, and electrokinetic SP. The algorithm is based on a mechanistic description of nonequilibrium thermodynamics that enables its coupling with a fluid flow simulator to quantify the effects of continuously varying properties within permeable formations due to mud-filtrate invasion. Numerical modeling of SP measurements acquired under complex petrophysical and geometric conditions enables uncertainty quantification in the estimation of formation-water resitivity, location of bed boundaries, or detection of permeable beds while accounting for shoulder-bed effects, borehole deviation, and borehole eccentricity. Our results indicate that for well trajectories with a relative dip of less than 30°, the assumption of perpendicular beds does not entail significant errors in SP-related calculations, thereby reducing CPU time by a factor of at least 1.76. In vertical wells, SP provides the best resolution possible because deviated wells or dipping beds result in more extended and pronounced shoulder-bed effects. Furthermore, electrokinetic effects can be neglected for commonly used pressure overbalance ranges. In cases in which electrokinetic contributions are not negligible, we conclude that they are more significant when the rock permeability is in the two-figure millidarcy range. Finally, the simulation algorithm enables hypothesis testing to determine the origin and conditions under which SP shale-baseline shifts may occur. The latter shifts can signal vertical variations in salt concentration, which are crucial in the estimation of water saturation and detection of aquifer compartments.

Onsager-Symmetry Obeyed in Athermal Mesoscopic Systems: Two-Phase Flow in Porous Media

We compute the fluid flow time-correlation functions of incompressible, immiscible two-phase flow in porous media using a 2D network model. Given a properly chosen representative elementary volume, the flow rate distributions are Gaussian and the integrals of time correlation functions of the flows are found to converge to a finite value. The integrated cross-correlations become symmetric, obeying Onsager's reciprocal relations. These findings support the proposal of a non-equilibrium thermodynamic description for two-phase flow in porous media.

Conservation laws and work fluctuation relations in chemical reaction networks.

We formulate a nonequilibrium thermodynamic description for open chemical reaction networks (CRNs) described by a chemical master equation. The topological properties of the CRN and its conservation laws are shown to play a crucial role. They are used to decompose the entropy production into a potential change and two work contributions, the first due to time dependent changes in the externally controlled chemostats concentrations and the second due to flows maintained across the system by nonconservative forces. These two works jointly satisfy a Jarzynski and Crooks fluctuation theorem. In the absence of work, the potential is minimized by the dynamics as the system relaxes to equilibrium and its equilibrium value coincides with the maximum entropy principle. A generalized Landauer's principle also holds: the minimal work needed to create a nonequilibrium state is the relative entropy of that state to its equilibrium value reached in the absence of any work.

Kinetics and thermodynamics of a driven open quantum system.

Redfield theory provides a closed kinetic description of a quantum system in weak contact with a very dense reservoir. Landau-Zener theory does the same for a time-dependent driven system in contact with a sparse reservoir. Using a simple model, we analyze the validity of these two theories by comparing their predictions with exact numerical results. We show that despite their a priori different range of validity, these two descriptions can give rise to an identical quantum master equation. Both theories can be used for a nonequilibrium thermodynamic description, which we show is consistent with exact thermodynamic identities evaluated in the full system-reservoir space. We emphasize the importance of properly accounting for the system-reservoir interaction energy and of operating in regimes where the reservoir can be considered as close to ideal.

Generalized boundary conditions for spin transfer

We develop a comprehensive description of static and dynamic spin-transfer torque at interfaces between a normal metal and a magnetic material. Specific examples of the latter include ferromagnets, collinear and noncollinear antiferromagnets, general ferrimagnets, and spin glasses. We study the limit of the exchange-dominated interactions, so that the full system is isotropic in spin space, apart from a possible symmetry-breaking order. A general such interface yields three coefficients (corresponding to three independent generators of rotations) generalizing the well-established notion of the spin-mixing conductance, which pertains to the collinear case. We develop a nonequilibrium thermodynamic description of the emerging interfacial spin transfer and its effect on the collective spin dynamics, while circumventing the usual discussion of spin currents and net spin dynamics. Instead, our focus is on the dissipation and work effectuated by the interface. Microscopic scattering-matrix based expressions are derived for the generalized spin-transfer coefficients.

Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics

We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations with mass action kinetics. Our most general framework considers open networks driven by time-dependent chemostats. The energy and entropy balances are established and a nonequilibrium Gibbs free energy is introduced. The difference between this latter and its equilibrium form represents the minimal work done by the chemostats to bring the network to its nonequilibrium state. It is minimized in nondriven detailed-balanced networks (i.e., networks that relax to equilibrium states) and has an interesting information-theoretic interpretation. We further show that the entropy production of complex-balanced networks (i.e., networks that relax to special kinds of nonequilibrium steady states) splits into two non-negative contributions: one characterizing the dissipation of the nonequilibrium steady state and the other the transients due to relaxation and driving. Our theory lays the path to study time-dependent energy and information transduction in biochemical networks.Received 23 February 2016DOI:https://doi.org/10.1103/PhysRevX.6.041064Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChemical kinetics, dynamics & catalysisNonequilibrium & irreversible thermodynamicsNonequilibrium statistical mechanicsStatistical PhysicsNonlinear DynamicsNetworksInterdisciplinary Physics

A discussion: Why do the free, shielding charges really exist at the surface of a ferroelectric?

ABSTRACTThe classical explanation of the shielding charges at the surface of a ferroelectric was looked back at first. Then based on the non-equilibrium (or irreversible) thermodynamic description of ferroelectric phase transitions, a new explanation of that was given out. They agree with each other. In particular, the former is a special case of the latter.

Non-equilibrium Thermodynamic Theory of Ferroelectric Phase Transitions

In this review, the non-equilibrium (or irreversible) thermodynamic theory of ferroelectric phase transitions was expounded systematically. Firstly, the limitations of the classical thermodynamic theory of ferroelectric phase transitions (known as the Landau-Devonshire theory) were reviewed critically. The unpleasant consequence caused by the metastable states hypothesis, and the evidence for the non-existence of metastable states i.e. the logical conflict, and the evidence for the existence of stationary states were shown. Secondly, the non-equilibrium thermodynamic description of (especially the first-order) ferroelectric phase transitions was given. The evolving, local characteristics of ferroelectric phase transitions were described well by using the principle of minimum entropy production and the generalized Onsager reciprocal relations. The thermo-electric coupling case is a reduced one of the thermo-electro-mechanical coupling case. In the realm of non-equilibrium thermodynamics, the relation between the latent heat and the polarization was given, too. Thirdly, the non-equilibrium thermodynamic explanation of the irreversibility of ferroelectric phase transitions, i.e. the thermal hysteresis and the domain occurrences in ferroelectrics, was given. At last, some concluding remarks were made and we looked forward to some possible developments.

Non-equilibrium thermodynamics analysis of transcriptional regulation kinetics

Abstract Gene expression in eukaryotic cells is an extremely complex and interesting phenomenon whose dynamics are controlled by a large number of subtle physicochemical processes commonly described by means of gene regulatory networks. Such networks consist in a series of coupled chemical reactions, conformational changes, and other biomolecular processes involving the interaction of the DNA molecule itself with a number of proteins usually called transcription factors as well as enzymes and other components. The kinetics behind the functioning of such gene regulatory networks are largely unknown, though its description in terms of non-equilibrium thermodynamics has been discussed recently. In this work we will derive general kinetic equations for a gene regulatory network from a non-equilibrium thermodynamical description and discuss its use in understanding the free energy constrains imposed in the network structure. We also will discuss explicit expressions for the kinetics of a simple model of gene regulation and show that the kinetic role of mRNA decay during the RNA synthesis stage (or transcription) is somehow limited due to the comparatively low values of decay rates. At the level discussed here, this implies a decoupling of the kinetics of mRNA synthesis and degradation a fact that may become quite useful when modeling gene regulatory networks from experimental data on whole genome gene expression.

The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation.

We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their "far from equilibrium behavior," hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative "external vector field" whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the "plasticity property" of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.

Quantum information approach to electronic equilibria: molecular fragments and non-equilibrium thermodynamic description

The quantum-generalized Information Theory is applied to explore molecular equilibrium states by using the resultant information content of electronic states, determind by the classical (probability based) measures and their non-classical (phase/current related) complements, in the extremum entropy/information principles. The “vertical” (probability-constrained) entropic rules are investigated within the familiar Levy and Harriman–Zumbach–Maschke constructions of Density Functional Theory. A close parallelism between the vertical maximum-entropy and minimum-energy principles in quantum mechanics and their thermodynamic analogs is emphasized and a relation between the probability and phase distributions in the “horizontal” (probability-unconstrained) phase-equilibria is examined. These solutions are shown to involve the spatial phase contribution related to the system electron density.The complete specification of the equilibrium states of molecular/promolecular fragments, including the subsystem density and the equilibrium phase of the system as a whole, is advocated and illustrated for bonded hydrogens in $$\hbox {H}_{2}$$ . Elements of the non-equilibrium thermodynamic description of molecular systems are formulated. They recognize the independent probability and phase state parameters, the associated currents, and their contributions to the quantum entropy density and its current. The phase and entropy continuity equations are explored and the local sources of these quantities are identified.

On phase/current components of entropy/information descriptors of molecular states

Quantum-generalised descriptors of the information content of electronic states in molecules are proposed, in which non-classical (current) terms complement classical (probability) functionals of the ordinary information theory. The relation between densities of the familiar classical Fisher and Shannon information/entropy measures is applied to determine their non-classical complements. The quantum supplement of the classical Shannon entropy describes the average magnitude of the phase distribution, while the current term in the Fisher measure accounts for the gradient content of the state phase function. Illustrative applications of these quantum information concepts are presented and thermodynamical analogies are commented upon. The particle-density-constrained (vertical) and -unconstrained (horizontal) equilibria in molecules and their fragments are explored and the corresponding equilibrium ‘thermodynamic’ phases are determined. A separation of the density (modulus) and current (phase) factors of general many-electron states is effected using the Harriman–Zumbach–Maschke construction of antisymmetric states yielding the specified electron density. The phenomenological framework in spirit of the non-equilibrium thermodynamical description is proposed. It accounts for both the density and current degrees of freedom of molecular states. The associated entropy source in the information continuity equation is derived.

Nonequilibrium chemistry in confined environments: A lattice Brusselator model

In this work, we study the effect of molecular crowding on a typical example of a chemical oscillator: the Brusselator model. We adopt to this end a nonequilibrium thermodynamic description, in which the size of particles is introduced via a lattice gas model. The impenetrability and finite volume of the species are shown to affect both the reaction rates and the diffusion terms in the evolution equations for the concentrations. The corrected scheme shows a more complex dynamical behavior than its ideal counterpart, including bistability and excitability. These results help to shed light on recent experimental and computational studies in biochemistry and surface chemistry, in which it was shown that confined environments may greatly affect chemical dynamics.

Mesoscopic non-equilibrium thermodynamic analysis of molecular motors

We show that the kinetics of a molecular motor fueled by ATP and operating between a deactivated and an activated state can be derived from the principles of non-equilibrium thermodynamics applied to the mesoscopic domain. The activation by ATP, the possible slip of the motor, as well as the forward stepping carrying a load are viewed as slow diffusion along a reaction coordinate. Local equilibrium is assumed in the reaction coordinate spaces, making it possible to derive the non-equilibrium thermodynamic description. Using this scheme, we find expressions for the velocity of the motor, in terms of the driving force along the spacial coordinate, and for the chemical reaction that brings about activation, in terms of the chemical potentials of the reactants and products which maintain the cycle. The second law efficiency is defined, and the velocity corresponding to maximum power is obtained for myosin movement on actin. Experimental results fitting with the description are reviewed, giving a maximum efficiency of 0.45 at a myosin headgroup velocity of 5 × 10(-7) m s(-1). The formalism allows the introduction and test of meso-level models, which may be needed to explain experiments.

Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density functional formulation and nature of steady-state forces

The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum statistical mechanics provide consistent but computational costly approaches; alternatively, the use of density-dependent ballistic-transport calculations (e.g., Lang 1995 Phys. Rev. B 52 5335), here denoted ‘DBT’, provides computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest-order approximation to an exact nonequilibrium thermodynamic density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy which, generally, must be treated as an implicit solution of the fully interacting many-body dynamics. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that the uniqueness-of-density proof from a closely related Lippmann–Schwinger collision density functional theory (Hyldgaard 2008 Phys. Rev. B 78 165109) makes it possible to express the variational nonequilibrium thermodynamic description as a single-particle formulation based on universal electron-density functionals; the full nonequilibrium single-particle formulation improves the DBT method, for example, by a more refined account of Gibbs free energy effects. I illustrate a formal evaluation of the zero-temperature thermodynamic grand potential value which I find is closely related to the variation in the scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the difference between the here-presented exact thermodynamic forces and the often-used electrostatic forces. Finally the paper documents an inherent adiabatic nature of the thermodynamic forces and observes that these are suited for a nonequilibrium implementation of the Born–Oppenheimer approximation.

Thermodynamic approach of supercontinuum generation

This paper is aimed at providing an overview on recent theoretical and experimental works in which a thermodynamic description of the incoherent regime of supercontinuum generation has been formulated. On the basis of the wave turbulence theory, we show that this highly nonlinear and quasi-continuous-wave regime of supercontinuum generation is characterized by two different phenomena. (i) A process of optical wave thermalization ruled by the four-wave mixing effects: The spectral broadening inherent to supercontinuum generation is shown to result from the natural tendency of the optical field to reach its thermodynamic equilibrium state, i.e., the state of maximum nonequilibrium entropy. This approach also reveals the existence of a thermodynamic phase-matching. (ii) The generation of spectral incoherent solitons induced by the Raman effect in the low frequency part of the supercontinuum spectrum. Contrary to conventional solitons, spectral incoherent solitons do not exhibit a confinement in the space–time domain, but solely in the frequency domain. They owe their existence to the causality property underlying the Raman response function. Both phenomena of optical wave thermalization and spectral incoherent solitons are described in detail by the wave turbulence theory. In this way, we provide a unified nonequilibrium thermodynamic description of the incoherent regime of supercontinuum generation.

Nonequilibrium Thermodynamics of Cell Signaling

Signal transduction inside and across the cells, also called cellular signaling, is key to most biological functions and is ultimately related with both life and death of the organisms. The processes giving rise to the propagation of biosignals are complex and extremely cooperative and occur in a far-from thermodynamic equilibrium regime. They are also driven by activation kinetics strongly dependent on local energetics. For these reasons, a nonequilibrium thermodynamical description, taking into account not just the activation of second messengers, but also transport processes and dissipation is desirable. Here we present a proposal for such a formalism, that considers cells as small thermodynamical systems and incorporates the role of fluctuations as intrinsic to the dynamics in a spirit guided by mesoscopic nonequilibrium thermodynamics. We present also a minimal model for cellular signaling that includes contributions from activation, transport, and intrinsic fluctuations. We finally illustrate its feasibility by considering the case of FAS signaling which is a vital signal transduction pathway that determines either cell survival or death by apoptosis.