Statistical Mechanics of Open Systems

We have generalized Kubo's treatment of isolated nonequilibrium systems to open systems in contact with thermal reservoirs. When the system is in contact with one reservoir and is subject to a weak external field, the deviation of the average of any quantity from its equilibrium value is related to a time-correlation function which incorporates the effect of the reservoir. A corollary is an isothermal fluctuation-dissipation theorem, which gives an explicit expression in terms of a time-correlation function for the rate at which energy flows from the driving field into the reservoir via the system. As an application, we compute the complex conductivity of a Lorentz gas. We also obtain an expression for the stationary nonequilibrium distribution of a system in contact with several reservoirs at slightly differing temperatures and chemical potentials. The Onsager coefficients, which relate the heat and particle fluxes to the differences among the reservoir parameters, are then explicitly expressed in terms of suitable time-correlation functions and their symmetry is exhibited. The validity of perturbation theory in finding the linear deviation from equilibrium of the $\Gamma$-space ensemble density is also discussed.