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

Abstract

In a previous paper (Ryazanov (2011)) with the joint statistical distribution for the energy and lifetime (time to achieve a given level of a stochastic process for energy of system) to derive thermodynamic relationships, clarifying similar expressions of extended irreversible thermodynamics we used an exponential distribution of lifetime. In this paper, we explore a more realistic expression for the distribution of time to achieve a given level of a stochastic process for energy of system (or relaxation times or lifetimes), and we analyse how such distribution affects the corresponding expressions of nonequilibrium entropy, temperature, and entropy production.

Gibbs Thermodynamics of the Renninger-Wilemski Problem

“…The object of further investigation will be the cluster of a liquid phase which is dense and compact contrast to a vapor phase. So, we will omit the index , use ] instead of , and speak about chemical potentials instead of differences in chemical potentials 5 .…”

“…The importance of nucleation initiates investigations from Wilson's experiments [1][2][3] up to modern investigations. Thermodynamic aspects of investigations occupy an important place in this field considering not only the fundamental question of stationarity (see to clarify it, e.g., [4,5]), but also the problems of smallness of characteristic embryos and corrections appeared because of its sizes and shapes [6]. The results given by thermodynamics immediately lead to quantitative description of kinetics [7] and can be included into consideration of some rather complex aggregates with very specific properties [8].…”

Superstatistics and Lifetime

“…But below we consider the stationary case, for which relations (2)-( 5) are satisfied with a certain approximation. A consideration of the general non-stationary case using queuing theory is given in [38][39][40]. In [39] it is shown that the argument s from ( 2)-( 3), ( 5) is written as a function of s, the argument is replaced, s→D(α=s)=f(s)~exp(-U/kBTe).…”

“…A consideration of the general non-stationary case using queuing theory is given in [38][39][40]. In [39] it is shown that the argument s from ( 2)-( 3), ( 5) is written as a function of s, the argument is replaced, s→D(α=s)=f(s)~exp(-U/kBTe). The function Q(s) from ( 2)-( 5) turns out to be a function of the form Q[D(α)], U is the additional potential energy received by the system, kB is the Boltzmann constant, Te is the absolute temperature.…”