Nonequilibrium Thermodynamics Based on the DistributionsContaining Lifetime as a Thermodynamic Parameter

Abstract

To describe the nonequilibrium states of a system, we introduce a new thermodynamic parameter—the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a system by specifying the stochastic processes are written down. The change in the lifetime values by interaction with environment is expressed in terms of fluxes and sources. The expressions for the nonequilibrium entropy, temperature, and entropy production are obtained, which at small values of fluxes coincide with those derived within the frame of extended irreversible thermodynamics. The explicit expressions for the lifetime of a system and its thermodynamic conjugate are obtained.

Nonequilibrium Thermodynamics and Distributions Time to Achieve a Given Level of a Stochastic Process for Energy of System

“…In [1] expressions for a nonequilibrium entropy S, entropy production σ, nonequilibrium temperature, and generalized transport equations for thermodynamic fluxes were proposed, taking into account a given distribution of internal relaxation times (or lifetimes) of the variables of the system. In the theory of random processes such values are called time to achieve a given level of the variables of the system (or the first-passage-time problems or escape time).…”

“…In the theory of random processes such values are called time to achieve a given level of the variables of the system (or the first-passage-time problems or escape time). In [1] for this quantity we used the term lifetime. These expressions generalize similar expressions of the extended irreversible thermodynamics (EIT) [2], a theory which takes into account the nonvanishing character of the relaxation time of the heat flux and other thermodynamic fluxes.…”

“…These expressions generalize similar expressions of the extended irreversible thermodynamics (EIT) [2], a theory which takes into account the nonvanishing character of the relaxation time of the heat flux and other thermodynamic fluxes. In [1] we proposed to take into consideration not only a single or a few relaxation time, but a whole distribution of relaxation times, generalizing in this way the previous proposals of EIT.…”

“…Approach [1] was based on the distribution containing lifetime as a thermodynamic parameter of the form…”

“…The expression (2) can be obtained from the algorithm of phase coarsening of the complex systems (Appendix 2 [1]). The distribution in the form (2) is valid for the existence of the weak ergodicity in a system.…”