Infimum Law and First-Passage-Time Fluctuation Theorem for Entropy Production
Year: 2016
Type: preprint
Abstract: We derive an infimum law and a first-passage-time fluctuation theorem for entropy production of stochastic processes at steady state. We show that the ratio between the probability densities of the first-passage time to produce $S_{\rm tot}$ of entropy and of the first-passage time to produce $-S_{\rm tot}$ of entropy equals $e^{S_{\rm tot}/k}$, with $k$ Boltzmann's constant. This first-passage-time fluctuation relation is valid for processes with one or higher order passages. In addition, we derive universal bounds for the infimum statistics of entropy production using the fact that at steady state $e^{-S_{\rm tot}/k}$ is a martingale process. We show that the mean value of the entropy-production infimum obeys $\langle{\rm inf}\:S_{\rm tot}\rangle\geq -k$ and derive a bound on the cumulative distribution of entropy-production infima. Our results are derived using a measure-theoretic formalism of stochastic thermodynamics. We illustrate our results with a drift-diffusion process and with numerical simulations of a Smoluchowski-Feynman ratchet.
Source: arXiv (Cornell University)
Authors: Izaak Neri, Édgar Roldán, Frank Jülicher
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2336932612