Analysis of Trajectory Entropy for Continuous StochasticProcesses at Equilibrium.

The analytical expression for thetrajectory entropy of the overdampedLangevin equation is derived via two approaches. The first route goesthrough the Fokker–Planck equation that governs the propagationof the conditional probability density, while the second method goesthrough the path integral of the Onsager–Machlup action. Theagreement of these two approaches in the continuum limit underscoresthe equivalence between the partial differential equation and thepath integral formulations for stochastic processes in the contextof trajectory entropy. The values obtained using the analytical expressionare also compared with those calculated with numerical solutions forarbitrary time resolutions of the trajectory. Quantitative agreementis clearly observed consistently across different models as the timeinterval between snapshots in the trajectories decreases. Furthermore,analysis of different scenarios illustrates how the deterministicand stochastic forces in the Langevin equation contribute to the variationin dynamics measured by the trajectory entropy. [ABSTRACT FROM AUTHOR]