The unreasonable effectiveness of equilibrium-like theory for interpreting non-equilibrium experiments

TL;DR

This paper demonstrates that equilibrium-like theories can effectively interpret non-equilibrium single molecule experiments, revealing simple, time-independent relations that facilitate rapid thermodynamic analysis.

Contribution

It introduces a heuristic example showing equilibrium results emerge from non-equilibrium phenomena and generalizes this via the central limit theorem, highlighting practical applications.

Findings

Equilibrium-like relations can describe non-equilibrium processes.

Time-independent equations enable quick thermodynamic parameter estimation.

Mechanical equilibrium at each instant underpins the observed relations.

Abstract

There has been great interest in applying the results of statistical mechanics to single molecule experiements. Recent work has highlighted so-called non-equilibrium work-energy relations and Fluctuation Theorems which take on an equilibrium-like (time independent) form. Here I give a very simple heuristic example where an equilibrium result (the barometric law for colloidal particles) arises from theory describing the {\em thermodynamically} non-equilibrium phenomenon of a single colloidal particle falling through solution due to gravity. This simple result arises from the fact that the particle, even while falling, is in {\em mechanical} equilibrium (gravitational force equal the viscous drag force) at every instant. The results are generalized by appeal to the central limit theorem. The resulting time independent equations that hold for thermodynamically non-equilibrium (and even non-stationary) processes offer great possibilities for rapid determination of thermodynamic parameters from single molecule experiments.