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A recent result, relating the (irreversible) work performed on a system during a non-quasistatic process, to the Helmholtz free energy difference between two equilibrium states of the system, is discussed. A proof of this result is given…
We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be…
Life is characterized by a myriad of complex dynamic processes allowing organisms to grow, reproduce, and evolve. Physical approaches for describing systems out of thermodynamic equilibrium have been increasingly applied to living systems,…
The fundamental dynamic stability of heat conduction theories beyond Fourier is analyzed in the framework of nonequilibrium thermodynamics. It is shown, that the thermodynamic framework, concave entropy and nonnegative entropy production,…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
A thermodynamic expression for the analog of the canonical ensemble for nonequilibrium systems is described based on a purely information theoretical interpretation of entropy. As an application, it is shown that this nonequilibrium…
We consider two types of the time-dependent Ginzburg-Landau equation in 2D bounded domains: the heat-flow equation and the Schroedinger equation. The system of ordinary differential equations is obtained that describes the evolution of the…
A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a…
There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for…
Critical phenomena in non-equilibrium systems have been studied by means of a wide variety of theoretical and experimental approaches. Mode-coupling, renormalization group, complex Lie algebras and diagrammatic techniques are some of the…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
We report that population dynamics in fluctuating environment accompanies mathematically equivalent structure to steady state thermodynamics. By employing the structure, population growth in fluctuating environment is decomposed into…
Following the analytic approach to thermodynamics developed by Stueckelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations…
All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory which accounts for interactions between chemical species within a…
Consider at a finite temperature $T$ a superfluid moving with a velocity $v$ relative to the thermal bath or its normal component. From Landau's argument there exists a critical $v_c (T)$ beyond which excitations can be spontaneously…
Using the contemporary thermodynamic equations of elastic solids leads to contradictions with the fundamental statements of thermodynamics. Two examples are presented to expose the inconsistencies. In example one the internal energy between…
An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is…
Growing economic inequalities are observed in several countries throughout the world. Following Pareto, the power-law structure of these inequalities has been the subject of much theoretical and empirical work. But their nonequilibrium…
We consider a macroscopic system in contact with boundary reservoirs and/or under the action of an external field. We discuss the case in which the external forcing depends explicitly on time and drives the system from a nonequilibrium…
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…