Statistical forces from close--to--equilibrium media

TL;DR

This paper explores how statistical forces on probes in near-equilibrium media are affected by nonequilibrium conditions, linking energetic, thermodynamic, and dynamical aspects to provide new insights and measurement methods.

Contribution

It introduces a general framework connecting nonequilibrium corrections to statistical forces with excess work and thermodynamic quantities, extending recent theoretical results.

Findings

Statistical force corrections relate to excess work in nonequilibrium media.

Point attractors align with minimum entropy production predictions.

Proposes a method to measure dynamical activity via statistical forces.

Abstract

We discuss the physical meaning and significance of statistical forces on quasi-static probes in first order around detailed balance for driven media. Exploiting the quasi-static energetics and the structure of (McLennan) steady nonequilibrium ensembles, we find that the statistical force obtains a nonequilibrium correction deriving from the excess work of driving forces on the medium in its relaxation after probe displacement. This reformulates, within a more general context, the recent result by N. Nakagawa (Phys. Rev. E 90, 022108 (2014)) on thermodynamic aspects of weakly nonequilibrium adiabatic pumping. It also proposes a possible operational tool for accessing some excess quantities in steady state thermodynamics. Furthermore, we show that the point attractors of a (macroscopic) probe coupled to a weakly driven medium realize the predictions of the minimum entropy production principle. Finally, we suggest a method to measure the relative dynamical activity through different transition channels, via the measurement of the statistical force induced by a suitable driving.