Hidden slow degrees of freedom and fluctuation theorems: an analytically solvable model

Abstract

In some situations in stochastic thermodynamics not all relevant slow degrees of freedom are accessible. Consequently, one adopts an effective description involving only the visible degrees of freedom. This gives rise to an apparent entropy production that violates standard fluctuation theorems. We present an analytically solvable model illustrating how the fluctuation theorems are modified. Furthermore, we define an alternative to the apparent entropy production: the marginal entropy production which fulfills the fluctuation theorems in the usual form. We show that the non-Markovianity of the visible process is responsible for the deviations in the fluctuation theorems.

arXiv comment18 pages, 4 figures

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• Entropy bound for time reversal markers
• Entropy production for partially observed harmonic systems
• Coarse-grained Second Order Response Theory
• Approximating microswimmer dynamics by active Brownian motion: Energetics and efficiency
• Inferring entropy production rate from partially observed Langevin dynamics under coarse-graining