Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

Relaxation to steady states of a binary liquid mixture around an optically heated colloid

We study the relaxation dynamics of a binary liquid mixture near a light-absorbing Janus particle after switching on and off illumination using experiments and theoretical models. The dynamics is controlled by the temperature gradient formed around the heated particle. Our results show that the relaxation is asymmetric: The approach to a nonequilibrium steady state is much slower than the return to thermal equilibrium. Approaching a nonequilibrium steady state after a sudden temperature change is a two-step process that overshoots the response of spatial variance of the concentration field. The initial growth of concentration fluctuations after switching on illumination follows a power law in agreement with the hydrodynamic and purely diffusive model. The energy outflow from the system after switching off illumination is well described by a stretched exponential function of time with characteristic time proportional to the ratio of the energy stored in the steady state to the total energy flux in this state.

Thermodynamic nonlinear response relation

The fluctuation-dissipation theorem connects equilibrium to mildly (linearly) perturbed situations in a thermodynamic manner: It involves the observable of interest and the entropy production caused by the perturbation. We derive a relation which connects responses of arbitrary order in perturbation strength to correlations of entropy production of lower order, thereby extending the fluctuation-dissipation theorem to cases far from equilibrium in a thermodynamic way. The relation is validated and studied for a four-state model which is coarse-grained to a non-Markovian two-state model.