The kinetic analog of Boltzmann’s principle

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Abstract
A general expression for the transition density of nonequilibrium diffusion processes is derived that is valid for non-Gaussian fluctuations. Using the thermodynamic principle, that relates the relative probability density of paths for absolutely continuous diffusion processes to the thermodynamic force, the kinetic analog of Boltzmann’s principle is derived. The transition density can be expressed in terms of the difference in entropies of the endpoints of the transition and the joint entropy. The gradient of the joint entropy is a measure of the strength of statistical correlations between nonequilibrium states and its difference (sum) between the thermodynamic forces determines the rates of growth (decay) of fluctuations. These rates are mirror images in time of one another and display a symmetry in past and future. The macroscopic laws of irreversible thermodynamics emerge in the exact balance of these two phenomena.