Steady adiabatic state: Its thermodynamics, entropy production, energy dissipation, and violation of Onsager relations

A class of statistical systems is considered where different degrees of fre edom have well-separated characteristic times, and are described by differe nt temperatures. The stationary state is a nonequilibrium state with a heat flow. A generalized statistical thermodynamics is constructed and a univer sal variational principle is proposed. Entropy production and energy dissip ation occur at a constant rate. To leading order in the small ratio of the characteristic times, there exists a universal relation between them. Onsag er relations in the context of heat transfer are also considered. They are always broken, except close to equilibrium.