Lifetime of System and Nonequilibrium Statistical Operator Method

Abstract

Lifetime of nonequilibrium statistical system is considered. It is supposed that the nonequilibrium statistical operator implicitly contains the lifetime. The operations of taking of invariant part, averaging on initial conditions used in works of D. N. Zubarev, temporary coarse‐graining (Kirkwood), choose of the direction of time are replaced by averaging on lifetime distribution. The expression for average lifetime of nonequilibrium system is derived. It is shown, that the nonequilibrium statistical operator in the formulation of D. N. Zubarev describes the lifetime of nonequilibrium systems.

Nonequilibrium statistical operators for systems with finite lifetime

“…The difference from the Zubarev form of NSO is of the order of the reciprocal lifetime of a system. In work [1] the new interpretation of a method of the Nonequilibrium Statistical Operator (NSO) [2,3] is given, in which NSO is treated as averaging of the quasi-equilibrium (or relevant [4,5]) statistical operator on the system past lifetime distribution and NSO rewritten aswhere H is hamiltonian, ln r(t) is the logarithm of the NSO, ln r q (t,0) is the logarithm of the quasi-equilibrium distribution; the first time argument indicates the time dependence of the values of the thermodynamic parameters F m ; the second time argument t 2 in r q (t 1 , t 2 ) denotes the time dependence through the Heizenberg representation for dynamical variables P m from which r q (t,0) can depend [1][2][3]. In [1] the function p q (u) = e exp {-eu} from [2,3] was interpreted as the probability distribution density of the lifetime of a system from the random moment t 0 of its birth till the current moment t; u = t -t 0 .…”

“…In work [1] the new interpretation of a method of the Nonequilibrium Statistical Operator (NSO) [2,3] is given, in which NSO is treated as averaging of the quasi-equilibrium (or relevant [4,5]) statistical operator on the system past lifetime distribution and NSO rewritten as ln r(t) = 0 ¥ ò p q (u) ln r q (t -u, -u)du, ln r q (t,0) = -F(t) -n å F n (t)P n ; (1) ln r q (t, t 1 ) = exp { -t 1 H/ih} ln r q (t, 0) exp {t 1 H/ih};…”

“…where H is hamiltonian, ln r(t) is the logarithm of the NSO, ln r q (t,0) is the logarithm of the quasi-equilibrium distribution; the first time argument indicates the time dependence of the values of the thermodynamic parameters F m ; the second time argument t 2 in r q (t 1 , t 2 ) denotes the time dependence through the Heizenberg representation for dynamical variables P m from which r q (t,0) can depend [1][2][3]. In [1] the function p q (u) = e exp {-eu} from [2,3] was interpreted as the probability distribution density of the lifetime of a system from the random moment t 0 of its birth till the current moment t; u = t -t 0 .…”

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].…”

Nonequilibrium statistical operator in the generalized hydrodynamics of fluids

“…In the investigations of such kind, the nonequilibrium statistical operator (NSO) method by Zubarev with some modifications is successfully applied [1][2][3][4]. In particular in [1,4] a new interpretation of the method of NSO is given, in which the operation of taking an invariant part in NSO is treated as the averaging of quasiequilibrium statistical operator on distribution of the past lifetime of a system…”