In this paper we propose a new model for the description of irreversible processes, which permits the construction of a Gibbs-type ensemble and the employment of the general techniques of statistical mechanics. The internal dynamics of the system that is engaged in the process is assumed to be described fully by its Hamiltonian. Its interaction with the driving reservoirs is described in terms of impulsive interactions (collisions). The reservoirs themselves possess definite temperatures, are inexhaustible, and free of internal gradients. The ensemble obeys an integro-differential equation in $\Gamma$ space, containing both the terms of the Liouville equation and a stochastic integral term that describes the collisions with the reservoirs. It is shown in this paper (1) that the ensemble will approach canonical distribution in the course of time in the presence of a single driving reservoir, (2) that it will approach a stationary nonequilibrium distribution in the presence of several reservoirs at different temperatures, and (3) that in the latter case, and for small temperature differences, Onsager's reciprocal relations are satisfied by the stationary distribution.

• Received 23 March 1955

DOI:https://doi.org/10.1103/PhysRev.99.578