Showing papers on "Non-equilibrium thermodynamics published in 2010"

Three Detailed Fluctuation Theorems

Abstract: The total entropy production of a trajectory can be split into an adiabatic and a nonadiabatic contribution, deriving, respectively, from the breaking of detailed balance via nonequilibrium boundary conditions or by external driving. We show that each of them, the total, the adiabatic, and the nonadiabatic trajectory entropy, separately satisfies a detailed fluctuation theorem.

Three faces of the second law. I. Master equation formulation.

Abstract: We propose a formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second law occurs in this description leading to three second-law-like relations. The general results are illustrated on specific solvable models. The present paper uses a master equation based approach.

Fluctuation-dissipation theorem in nonequilibrium steady states

Abstract: In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to energy. For a nonequilibrium steady state (NESS), the corresponding FDT is shown to involve in the correlation function a variable that is conjugate with respect to entropy. By splitting up entropy production into one of the system and one of the medium, it is shown that for systems with a genuine equilibrium state the FDT of the NESS differs from its equilibrium form by an additive term involving total entropy production. A related variant of the FDT not requiring explicit knowledge of the stationary state is particularly useful for coupled Langevin systems. The a priori surprising freedom apparently involved in different forms of the FDT in a NESS is clarified.

Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers

Abstract: Equilibrium Thermodynamics: A Review.- Classical Irreversible Thermodynamics.- Coupled Transport Phenomena.- Chemical Reactions and Molecular Machines.- Finite-Time Thermodynamics.- Instabilities and Pattern Formation.- Extended Irreversible Thermodynamics.- Theories with Internal Variables.- Rational Thermodynamics.- Hamiltonian Formalisms.- Mesoscopic Thermodynamic Descriptions.

Relations between the fractional Stokes-Einstein and Nernst-Einstein equations and velocity correlation coefficients in ionic liquids and molten salts.

Abstract: It is often asserted that deviation from the Nernst−Einstein relation (NE) between the molar conductivity (Λ) and ion self-diffusion coefficients (Di) in ionic liquids (ILs) and molten salts is evidence for ion pairing. The NE was originally derived for noninteracting ions, as in an infinitely dilute electrolyte solution. In reality, mass, charge, momentum, and energy transport processes in ILs and molten salts involve correlated interionic collisions, caging, and vortex motions, as in any other dense liquid. Phenomenological theory using nonequilibrium thermodynamics and literature molecular dynamics simulations shows that deviations from the simple NE expression occur due to differences in cross-correlations of ionic velocities. ILs have also been shown, like molecular liquids generally, and model fluids such as the Lennard-Jones, to fit the fractional form of the Stokes−Einstein relation, Di/T ∝ (1/η)t and Λ ∝ (1/η)t, where η is the shear viscosity. Here, it is shown that when this is the case, the NE ...

Estimating dissipation from single stationary trajectories.

Abstract: In this Letter we show that the time reversal asymmetry of a stationary time series provides information about the entropy production of the physical mechanism generating the series, even if one ignores any detail of that mechanism. We develop estimators for the entropy production which can detect nonequilibrium processes even when there are no measurable flows in the time series.

On the Thermodynamics of Friction and Wear―A Review

Abstract: An extensive survey of the papers pertaining to the thermodynamic approach to tribosystems, particularly using the concept of entropy as a natural time base, is presented with a summary of the important contributions of leading researchers.

Free energy profiles from single-molecule pulling experiments

Abstract: Nonequilibrium pulling experiments provide detailed information about the thermodynamic and kinetic properties of molecules. We show that unperturbed free energy profiles as a function of molecular extension can be obtained rigorously from such experiments without using work-weighted position histograms. An inverse Weierstrass transform is used to relate the system free energy obtained from the Jarzynski equality directly to the underlying molecular free energy surface. An accurate approximation for the free energy surface is obtained by using the method of steepest descent to evaluate the inverse transform. The formalism is applied to simulated data obtained from a kinetic model of RNA folding, in which the dynamics consists of jumping between linker-dominated folded and unfolded free energy surfaces.

Exact solution for a diffusive nonequilibrium steady state of an open quantum chain

Abstract: We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends The obtained state is exact in the limit of weak driving while the expressions for one- and two-point correlations are exact for an arbitrary driving strength In the steady state the magnetization profile and the spin current display diffusive behavior The spin–spin correlation function, on the other hand, has long-range correlations which, though, decay to zero in either the thermodynamical limit or for equilibrium driving At zero dephasing a nonequilibrium phase transition occurs from a ballistic transport having short-range correlations to a diffusive transport with long-range correlations

An effective rate equation approach to reaction kinetics in small volumes: Theory and application to biochemical reactions in nonequilibrium steady-state conditions

Abstract: Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells.

Exact solution for a diffusive nonequilibrium steady state of an open quantum chain

Abstract: We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends. The obtained state is exact in the limit of weak driving while the expressions for one- and two-point correlations are exact for an arbitrary driving strength. In the steady state the magnetization profile and the spin current display diffusive behavior. Spin-spin correlation function on the other hand has long-range correlations which though decay to zero in either the thermodynamical limit or for equilibrium driving. At zero dephasing a nonequilibrium phase transition occurs from a ballistic transport having short-range correlations to a diffusive transport with long-range correlations.

Nonequilibrium thermodynamics of spacetime: The role of gravitational dissipation

Abstract: In [T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995).] it was shown that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. More recently, in the attempt to extend the same approach to the case of $f(R)$ theories of gravity, it was found that a nonequilibrium setting is indeed required in order to fully describe both this theory as well as classical general relativity (GR) [C. Eling, R. Guedens, and T. Jacobson, Phys. Rev. Lett. 96, 121301 (2006).]. Here, elaborating on this point, we show that the dissipative character leading to nonequilibrium spacetime thermodynamics is actually related---both in GR as well as in $f(R)$ gravity---to nonlocal heat fluxes associated with the purely gravitational/internal degrees of freedom of the theory. In particular, in the case of GR we show that the internal entropy production term is identical to the so-called tidal heating term of Hartle-Hawking. Similarly, for the case of $f(R)$ gravity, we show that dissipative effects can be associated with the generalization of this term plus a scalar contribution whose presence is clearly justified within the scalar-tensor representation of the theory. Finally, we show that the allowed gravitational degrees of freedom can be fixed by the kinematics of the local spacetime causal structure, through the specific equivalence principle formulation. In this sense, the thermodynamical description seems to go beyond Einstein's theory as an intrinsic property of gravitation.

Physical foundations of evolutionary theory

Abstract: The theory of evolution by natural selection is herein subsumed by the 2nd law of thermodynamics. The mathematical form of evolutionary theory is based on a re-examination of the probability concept that underlies statistical physics. Probability regarded as physical must include, in addition to isoenergic combinatorial configurations, also energy in conditional circumstances. Consequently, entropy as an additive logarithmic probability measure is found to be a function of the free energy, and the process toward the maximum entropy state is found equivalent to evolution toward the free energy minimum in accordance with the basic maxim of chemical thermodynamics. The principle of increasing entropy when given as an equation of motion reveals that expansion, proliferation, differentiation, diversification, and catalysis are all ways for a system to evolve toward the stationary state in its respective surroundings. Intriguingly, the equation of evolution cannot be solved when there remain degrees of freedom to consume the free energy, and hence evolutionary trajectories of a nonHamiltonian system remain intractable. Finally, when to-and-from flows of energy are balanced between a system and its surroundings, the system is at the Lyapunov-stable stationary state. The principle of maximal energy dispersal, equivalent to the maximal rate of entropy production, gives rise to the ubiquitous characteristics, conventions, and regularities found in nature, where thermodynamics makes no demarcation line between animate and inanimate.

Bidirectional single-electron counting and the fluctuation theorem

Abstract: We investigate theoretically and experimentally the full counting statistics of bidirectional singleelectron tunneling through a double quantum dot in a GaAs/GaAlAs heterostructure and compare with predictions of the fluctuation theorem (FT) for Markovian stochastic processes. We observe that the quantum point contact electrometer used to study the transport induces nonequilibrium shot noise and dot-level fluctuations and strongly modifies the tunneling statistics. As a result, the FT appears to be violated. We show that it is satisfied if the back-action of the electrometer is taken into account, and we provide a quantitative estimate of this effect. PACS numbers: 73.23.-b,73.23.Hk,72.70.+m,05.70.Ln According to the second law of thermodynamics, the entropy of a macroscopic system driven out of equilibrium increases with time until equilibrium is reached. Thus the dynamics of such a system is irreversible. In contrast, for a mesoscopic system performing a random trajectory in phase space and measured during a sufficiently short time, the entropy may either increase or decrease. The ‘Fluctuation Theorem’ (FT), which relies only on the microreversiblity of the underlying equation of motion, states that the probability distribution P�(�S) for processes increasing or decreasing the en= (�)=  

Thermodynamics in $f(R)$ gravity in the Palatini formalism

Abstract: We investigate thermodynamics of the apparent horizon in f(R) gravity in the Palatini formalism with non-equilibrium and equilibrium descriptions. We demonstrate that it is more transparent to understand the horizon entropy in the equilibrium framework than that in the non-equilibrium one. Furthermore, we show that the second law of thermodynamics can be explicitly verified in both phantom and non-phantom phases for the same temperature of the universe outside and inside the apparent horizon.

Entropy in Tribology: in the Search for Applications

Abstract: The paper discusses the concept of entropy as applied to friction and wear. Friction and wear are classical examples of irreversible dissipative processes, and it is widely recognized that entropy generation is their important quantitative measure. On the other hand, the use of thermodynamic methods in tribology remains controversial and questions about the practical usefulness of these methods are often asked. A significant part of entropic tribological research was conducted in Russia since the 1970s. Surprisingly, many of these studies are not available in English and still not well known in the West. The paper reviews various views on the role of entropy and self-organization in tribology and it discusses modern approaches to wear and friction, which use the thermodynamic entropic method as well as the application of the mathematical concept of entropy to the dynamic friction effects (e.g., the running-in transient process, stick-slip motion, etc.) and a possible connection between the thermodynamic and information approach. The paper also discusses non-equilibrium thermodynamic approach to friction, wear, and self-healing. In general, the objective of this paper is to answer the frequently asked question “is there any practical application of the thermodynamics in the study of friction and wear?” and to show that the thermodynamic methods have potential for both fundamental study of friction and wear and for the development of new (e.g., self-lubricating) materials.

Introduction to Nonequilibrium Statistical Mechanics with Quantum Field Theory

Abstract: In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson’s equation. The aims are threefold: (i) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (ii) to elucidate the hierarchy in describing nonequilibrium systems from Dyson’s equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (iii) to derive an expression of nonequilibrium entropy that evolves with time. In stage (i), we introduce nonequilibrium Green’s function and the self-energy uniquely on the roundtrip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green’s functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the selfconsistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym’s Φ-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Φ-derivable approximation, i.e., an issue of how to handle the “Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy”. Aim (ii) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog’s expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems can be handled microscopically with quantum field theory, including fluctuations. We also discuss a derivation of the quantum transport equations for electrons in electromagnetic fields based on the gauge-invariant Wigner transformation so that the Lorentz force is reproduced naturally. As for (iii), the Gibbs entropy of equilibrium statistical mechanics suffers from the flaw that it does not evolve in time. We show here that a microscopic expression of nonequilibrium dynamical entropy can be derived from the quantum transport equations so as to be compatible with the law of increase in entropy as well as equilibrium statistical mechanics. Subject Index: 052, 056, 062, 356, 512

Introduction to Nonequilibrium Statistical Mechanics with Quantum Field

Abstract: In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (i) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (ii) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (iii) to derive an expression of nonequilibrium entropy that evolves with time. In stage (i), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Phi-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Phi-derivable approximation, i.e., an issue of how to handle the "Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy".

A basic introduction to the thermodynamics of the Earth system far from equilibrium and maximum entropy production

Abstract: The Earth system is remarkably different from its planetary neighbours in that it shows pronounced, strong global cycling of matter. These global cycles result in the maintenance of a unique thermodynamic state of the Earth's atmosphere which is far from thermodynamic equilibrium (TE). Here, I provide a simple introduction of the thermodynamic basis to understand why Earth system processes operate so far away from TE. I use a simple toy model to illustrate the application of non-equilibrium thermodynamics and to classify applications of the proposed principle of maximum entropy production (MEP) to such processes into three different cases of contrasting flexibility in the boundary conditions. I then provide a brief overview of the different processes within the Earth system that produce entropy, review actual examples of MEP in environmental and ecological systems, and discuss the role of interactions among dissipative processes in making boundary conditions more flexible. I close with a brief summary and conclusion.

Transport Properties of High-Temperature Jupiter-Atmosphere Components

Abstract: Transport properties of high-temperature helium and hydrogen plasmas as well as Jupiter atmosphere have been calculated for equilibrium and nonequilibrium conditions using higher approximations of the Chapman–Enskog method. A complete database of transport cross sections for relevant interactions has been derived, including minority species, by using both ab initio and phenomenological potentials. Inelastic collision integrals terms, due to resonant charge-exchange channels, have been also considered.

Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems

Abstract: A common assumption in the glass science community is that the entropy of a glass can be calculated by integration of measured heat capacity curves through the glass transition. Such integration assumes that glass is an equilibrium material and that the glass transition is a reversible process. However, as a nonequilibrium and nonergodic material, the equations from equilibrium thermodynamics are not directly applicable to the glassy state. Here we investigate the connection between heat capacity and configurational entropy in broken ergodic systems such as glass. We show that it is not possible, in general, to calculate the entropy of a glass from heat capacity curves alone, since additional information must be known related to the details of microscopic fluctuations. Our analysis demonstrates that a time-average formalism is essential to account correctly for the experimentally observed dependence of thermodynamic properties on observation time, e.g., in specific heat spectroscopy. This result serves as experimental and theoretical proof for the nonexistence of residual glass entropy at absolute zero temperature. Example measurements are shown for Corning code 7059 glass.

Extended Irreversible Thermodynamics: Evolution Equations

Abstract: Our general purpose is to propose a theory which goes beyond the classical formulation of irreversible thermodynamics (CIT) This is achieved by enlarging the space of basic independent variables through the introduction of non-equilibrium variables, such as the dissipative fluxes appearing in the balance equations of mass, momentum and energy The next step is to find evolution equations for these extra variables Whereas the evolution equations for the classical variables are given by the usual balance laws, no general criteria exist concerning the evolution equations of the dissipative fluxes, with the exception of the restrictions imposed on them by the second law of thermodynamics

Thermal boundary resistance from mode energy relaxation times: Case study of argon-like crystals by molecular dynamics

Abstract: We derive the mode spectrum of the thermal boundary resistance between two bodies having a temperature difference ΔT. A general expression of the time τ that defines the resistance is derived as the equilibrium autocorrelation of ΔT integrated over time. A further decomposition of this autocorrelation yields the resistance spectrum as equal to the mode relaxation time weighted by its energy mean square fluctuation. We then perform molecular dynamics simulations of argon like crystals in equilibrium and nonequilibrium regimes to prove the relevance of our model. This general method allows for deriving the resistance spectrum and therefore can yield key rules to control the exchanged heat flux.

Entropy Production of Cyclic Population Dynamics

Abstract: Entropy serves as a central observable in equilibrium thermodynamics. However, many biological and ecological systems operate far from thermal equilibrium. Here we show that entropy production can characterize the behavior of such nonequilibrium systems. To this end we calculate the entropy production for a population model that displays nonequilibrium behavior resulting from cyclic competition. At a critical point the dynamics exhibits a transition from large, limit-cycle-like oscillations to small, erratic oscillations. We show that the entropy production peaks very close to the critical point and tends to zero upon deviating from it. We further provide analytical methods for computing the entropy production which agree excellently with numerical simulations.