On equilibrium distributions and detailed balance relations in non-isothermal systems

The significance of the detailed balance principle and equilibrium solutions of the master equation is discussed from a thermodynamic point of view for isolated and isothermal systems. Starting from a master equation for all the time dependent degrees of freedom it is shown that the uniqueness of the equilibrium distribution as a stationary solution is ensured if the detailed rate constants are balanced with the aid of the distribution which maximizes the entropy subject to the thermodynamic constraints. This procedure should precede physical assumptions which simplify the original master equation, e.g. the assumption that rapidly relaxing modes can be described by canonical distribution functions.