Statistical Mechanics of Non-Equilibrium Systems. I: Extensive Property, Fluctuation and Non-Linear Response

Abstract

The existence of thermodynamic limits of non-equilibrium reduced density matrix and distribution function is proved on the following assumptions on initial states and temporal evolution of the system: The initial state is described by a canonical distribution, an effective Hamiltonian of which is the sum of local Hamiltonians and some averages of “local” operators are bounded. This proof yields an extension of Kubo's Ansatz on the extensive property of a macrovariable to quantal systems and to non-Markoffian macrovariables in stochastic models. A generating function (generalized thermodynamic potential) formalism is used effectively for discussing the above non-equilibrium problems. Non-linear response and fluctuation are also discussed in the above-mentioned scheme.