Universal Property of the Housekeeping Entropy Production

Abstract

The entropy production of a nonequilibrium system with broken detailed balance is a random variable whose mean value is nonnegative. Among the total entropy production, the housekeeping entropy production is associated with the heat dissipation in maintaining a nonequilibrium steady state. We derive a Langevin-type stochastic differential equation for the housekeeping entropy production. The equation allows us to define a housekeeping entropic time $\tau$. Remarkably, it turns out that the probability distribution of the housekeeping entropy production at a fixed value of $\tau$ is given by the Gaussian distribution regardless of system details. The Gaussian distribution is universal for any systems, whether in the steady state or in the transient state, whether they are driven by time-independent or time-dependent driving forces. We demonstrate the universal distribution numerically for model systems.

arXiv comment6 pages, 2 figures (v2) Sec. III are revised. Figures are updated

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• Martingale theory for housekeeping heat
• Universal Excursion and Bridge shapes in ABBM/CIR/Bessel processes
• Detailed fluctuation theorem bounds apparent violations of the second law
• Information bound for entropy production from the detailed fluctuation theorem
• Moment generating function bound from detailed fluctuation theorem
• Ubiquitous Dynamical Time Asymmetry in Measurements on Materials and Biological Systems
• Thermodynamic uncertainty relation in the overdamped limit with a magnetic Lorentz force