The law of action and reaction for the effective force in a nonequilibrium colloidal system

TL;DR

This paper investigates the effective forces between two test particles in a driven nonequilibrium colloidal system, revealing that the classical action-reaction law applies only to thermodynamic forces, not total mechanical forces.

Contribution

The study introduces an effective description of nonequilibrium steady states in colloidal systems and clarifies the conditions under which the action-reaction law holds.

Findings

Action-reaction law fails for total mechanical force from background particles.

The law holds for thermodynamic forces defined operationally.

Numerical simulations support the theoretical formulation.

Abstract

We study a nonequilibrium Langevin many-body system containing two 'test' particles and many 'background' particles. The test particles are spatially confined by a harmonic potential, and the background particles are driven by an external driving force. Employing numerical simulations of the model, we formulate an effective description of the two test particles in a nonequilibrium steady state. In particular, we investigate several different definitions of the effective force acting between the test particles. We find that the law of action and reaction does not hold for the total mechanical force exerted by the background particles, but that it does hold for the thermodynamic force defined operationally on the basis of an idea used to extend the first law of thermodynamics to nonequilibrium steady states.