Microscopic theory for the time irreversibility and the entropy production

Abstract

In stochastic thermodynamics, the entropy production of a thermodynamic system is defined by the irreversibility measured by the logarithm of the ratio of the path probabilities in the forward and reverse processes. We derive the relation between the irreversibility and the entropy production starting from the deterministic equations of motion of the whole system consisting of a physical system and a surrounding thermal environment. The physical system is driven by a nonconservative force. The derivation assumes the Markov approximation that the environmental degrees of freedom equilibrate instantaneously. Our approach concerns the irreversibility of the whole system not only the irreversibility of the physical system only. This approach provides a guideline for the choice of the proper reverse process to a given forward process. We demonstrate our idea with an example of a charged particle in the presence of a time-varying magnetic field.

Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force

“…Note that there is no unique way to choose odd parameters for the time-reversal process. For example, one may regard a magnetic field as an odd parameter, so change the sign of a magnetic field in the time-reverse dynamics [21,47]. On the other hand, one may keep the sign of the magnetic field for the irreversibility [48][49][50][51][52], where the † dynamics is identical to the original time-forward dynamics.…”

“…and ξ 0 (t 0 ) ≡ √ τξ(t) satisfying ξ 0 (t 0 )ξ 0 (t ′ 0 ) = δ(t 0 −t ′ 0 ). Equations (46) and (47) are then written in terms of the dimensionless variables and parameters as…”

Mandal, Klymko, and DeWeese Reply

“…In the mapped system, there is a momentumdependent force in addition to the damping force. As has been shown over the years [7][8][9], fluctuation relations for entropy production in this situation involve a new process that arises from the reversal of this additional momentum-dependent force. We have followed this established procedure in our work.…”

Thermodynamic uncertainty relation in the overdamped limit with a magnetic Lorentz force

“…Note that the Lorenz term is not included for the irreversible current, so the total entropy production here does not involve the so-called unconventional entropy production term and becomes the Clausius entropy in the steady state [60][61][62].…”