Complementarity relation for irreversible process derived from stochastic energetics

TL;DR

This paper derives a complementarity relation linking irreversible heat and process duration in classical Langevin systems, using stochastic energetics, highlighting a fundamental thermodynamic limit independent of the process path.

Contribution

It establishes a new complementarity relation for irreversible heat and time in Langevin systems, extending stochastic energetics to quantify thermodynamic constraints.

Findings

Irreversible heat and time satisfy Q_irr * Δt >= k_B T S_min.

S_min depends on initial and final control parameters, not the pathway.

The relation is derived for isothermal processes in Langevin dynamics.

Abstract

When the process of a system in contact with a heat bath is described by classical Langevin equation, the method of stochastic energetics [K. Sekimoto, J. Phys. Soc. Jpn. vol. 66 (1997) p.1234] enables to derive the form of Helmholtz free energy and the dissipation function of the system. We prove that the irreversible heat Q_irr and the time lapse $Delta t} of an isothermal process obey the complementarity relation, Q_irr {Delta t} >= k_B T S_min, where S_min depends on the initial and the final values of the control parameters, but it does not depend on the pathway between these values.