Surprisal analysis of dissipative Fokker-Planck dynamics in phase-space

Rajendran Saravanan and R.D. Levine

Physica A: Statistical Mechanics and its Applications, 2025, vol. 674, issue C

Abstract: We show that in well-characterized special cases, a maximal entropy-motivated approach can provide an exact description of the dynamics in phase space of a classical dissipative system such as governed by the Fokker-Planck equation. This is achieved by identifying a set of constraints which, when held constant in time, make the system stationary. Even when such a set is not possible in general it can be identified for special limits. An example is a double well potential in the limit of a high barrier between the two wells. Technically we show that the surprisal of the distribution can be expressed as a linear combination of the constraints. The time-dependent expansion coefficients are identified as the Lagrange multipliers needed to impose a distribution of maximal entropy. For an exact solution, the Lagrange multipliers satisfy a closed set of equations of motion. Unlike the reversible case where these equations are linear, the dissipation introduces non-linear terms. Even so, for an exact solution, the equations are integrable. The constraints are a basis for time-dependent constants of the motion. When it is not possible to identify an exact solution the maximal entropy formalism delivers a tight numerical approximation for the distribution. For the Kramers barrier crossing problem for a high barrier, the surprisal analysis correctly determines the branching fraction between the two wells.

Keywords: Information theory entropy; Surprisal analysis; Stochastic processes; Phase-space distribution; Kramers' activated crossings; Double-well potential (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125004388

DOI: 10.1016/j.physa.2025.130786

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