On the basis of the joint probability for the two states occurring at different times proposed by Onsager, the theory of Brownian motion is generalized to the case of isolated systems such as treated by “the thermodynamics of irreversible processes.” Fokker-Planck's and Langevin's equations are also generalized. When the deviations from thermal equilibrium are so small that the entropy of the system is expressible in a quadratic form with respect to its state variables, these equations are integrated, and the probability distribution for the state variables at each time is obtained.