Properties of the dissipation functions for passive and active systems

Harsh Soni
Phys. Rev. E 107, 014111 – Published 11 January 2023

Abstract

The dissipation function for a system is defined as the natural logarithm of the ratio between probabilities of a trajectory and its time-reversed trajectory, and its probability distribution follows a well-known relation called the fluctuation theorem. Using the generic Langevin equations, we derive the expressions of the dissipation function for passive and active systems. For passive systems, the dissipation function depends only on the initial and the final values of the dynamical variables of the system, not on the trajectory of the system. Furthermore, it does not depend explicitly on the reactive or dissipative coupling coefficients of the generic Langevin equations. In addition, we study a one-dimensional case numerically to verify the fluctuation theorem with the form of the dissipation function we obtained. For active systems, we define the work done by active forces along a trajectory. If the probability distribution of the dynamical variables is symmetric under time reversal, in both cases, the average rate of change of the dissipation function with trajectory duration is nothing but the average entropy production rate of the system and reservoir.

  • Figure
  • Received 26 September 2022
  • Revised 26 November 2022
  • Accepted 23 December 2022

DOI:https://doi.org/10.1103/PhysRevE.107.014111

©2023 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Harsh Soni

  • School of Physical Sciences, IIT Mandi, Kamand, Mandi, HP 175005, India

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Issue

Vol. 107, Iss. 1 — January 2023

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