The law of action and reaction for the effective force in a non-equilibrium colloidal system

We study a non-equilibrium 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. Using numerical simulations of the model, we formulate an effective description of the two test particles in a non-equilibrium 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 non-equilibrium steady states.