Entropy production for velocity-dependent macroscopic forces: the problem of dissipation without fluctuations

Abstract

In macroscopic systems, velocity-dependent phenomenological forces $F(v)$ are used to model friction, feedback devices or self-propulsion. Such forces usually include a dissipative component which conceals the fast energy exchanges with a thermostat at the environment temperature $T$, ruled by a microscopic Hamiltonian $H$. The mapping $(H,T)\to F(v)$ - even if effective for many purposes - may lead to applications of stochastic thermodynamics where an $incomplete$ fluctuating entropy production (FEP) is derived. An enlightening example is offered by recent macroscopic experiments where dissipation is dominated by solid-on-solid friction, typically modelled through a deterministic Coulomb force $F(v)$. Through an adaptation of the microscopic Prandtl-Tomlinson model for friction, we show how the FEP is dominated by the heat released to the $T$-thermostat, ignored by the macroscopic Coulomb model. This problem, which haunts several studies in the literature, cannot be cured by weighing the time-reversed trajectories with a different auxiliary dynamics: it is only solved by a more accurate stochastic modelling of the thermostat underlying dissipation.

6 pages, 3 figures

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• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• The Entropy Production of Ornstein-Uhlenbeck Active Particles: a path integral method for correlations
• Heat, temperature and Clausius inequality in a model for active brownian particles
• Clausius relation for active particles: what can we learn from fluctuations?
• Effective fluctuation and response theory
• Comment on "Entropy Production and Fluctuation Theorems for Active Matter"
• Revealing the Nonequilibrium Nature of a Granular Intruder: The Crucial Role of Non-Gaussian Behavior
• Entropy production by active particles: Coupling of odd and even functions of velocity
• Microscopic theory for the time irreversibility and the entropy production
• Thermodynamic uncertainty relations in the presence of non-linear friction and memory
• Diffusion Properties of a Brownian Ratchet with Coulomb Friction