Nonisothermal activation : nonlinear transport theory

We present the statistical mechanical foundation of nonisothermal stochastic processes, thereby generalizing Kramers' Fokker-Planck model for thermal activation and providing a microscopic context for Rolf Landauer's original ideas on state-dependent diffusion. By applying projection operator methods suitable for nonlinear mesoscopic systems coupled to a heat bath, we develop the theory of classical Brownian motion (in position and momentum) including the local temperature as a dynamical variable. The ensuing stochastic process involves a microcanonical effective mean force different from the free energy gradient, while the equilibrium potential is given by the availability. The effective spatial diffusion coefficient in the Smoluchowski limit is calculated. The microcanonical analysis corresponds to the case of small thermal conductance