Trajectory Entropy of Continuous Stochastic Processes at Equilibrium

Abstract

We propose to quantify the trajectory entropy of a dynamic system as the information content in excess of a free diffusion reference model. The space-time trajectory is now the dynamic variable and its path probability is given by the Onsager-Machlup action. For the time propagation of the over-damped Langevin equation, we solved the action path integral in the continuum limit and arrived at an exact analytical expression that emerged as a simple functional of the deterministic mean force and the stochastic diffusion. This work could have direct implications in chemical and phase equilibria, bond isomerization and conformational changes in biological macromolecules, as well transport problems in general.