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

TL;DR

This paper investigates how velocity-dependent forces in macroscopic systems relate to microscopic dissipation, highlighting that incomplete stochastic models overlook key entropy production contributions from the environment.

Contribution

It demonstrates that accurate stochastic modeling of the thermostat is essential to correctly account for entropy production in systems with velocity-dependent forces.

Findings

FEP is dominated by heat to the thermostat in friction models

Incomplete models underestimate entropy production

Proper stochastic modeling resolves dissipation ambiguities

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.