On nonlinear irreversible processes I

A functional integral expression of the two gate probability distribution function is obtained and the integral is performed in a “semiclassical” approximation. Based on this approximation, it is shown that the expression of the many gate probability distribution function in terms of two dissipation functions, which Onsager and Machlup presented before as the extension of Boltzmann's principle, is valid also for nonlinear processes with a slight modification of definition of the dissipation functions. Only the case that all the variables are even functions of time is treated for simplicity.