Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

Abstract

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter -the lifetime of a system. A 322, (2003), 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment. Superstatistics, introduced in works of Beck and Cohen [Physica

Superstatistics and Lifetime

“…For example, many results established for superstatistics and nonextensive statistical mechanics, are transferred to the description of complex systems by means of the distribution containing lifetime. Since thermodynamics with lifetime [4,5] is more general, than the theory of superstatistiks also it has more opportunities. Interesting is establishing the relation to a method of the nonequilibrium statistical operator of Zubarev [11] generalizing Gibbs distributions which as it was marked, it is possible to compare to the distributions containing lifetime, and nonextensive statistical mechanics [2][3], in which entropy is represented by means of the measures which are distinct from Boltzmann and Gibbs.…”

“…We have from (6)- (7) and (10) when At n=1 from correlations such as (11) it is possible to obtain the description of such nonequilibrium phenomena, as heat conductivity, mass transfer, the chemical reactions [4,5], close to the description by means of the Extended Irreversible Thermodynamics [17].…”

Nonequilibrium Statistical Operator for Systems of Finite Size

“…The lifetime of system is represented by fundamental value having a dual nature, related to both the external time flow and to the properties of the system. The relationship between the lifetime and the nonequilibrium statistical operator method was investigated in [57,58,59].…”

Neutron number first-passage time distribution and the reactor time constant

“…For this reason, the term "lifetime" from [1, 2] is not used in the present work. This quantity is described deterministically, though its nature is random because of the stochasticity of neutron processes.…”

“…We shall take account of the dynamical behavior of a nuclear reactor by introducing piecewise-continuous functions, as in [2]. Only the reactivity ρ(t) and neutron multiplication factor k(t) = [1 -ρ(t)] -1 are time-dependent.…”