Fluctuation-Response Relations

17 Apr 2021 17:27

A key result in statistical mechanics is what's known as the "fluctuation-dissipation" or "fluctuation-response" relation. Assemblages of particles in thermodynamic equilibrium actually fluctuate all the time. (Typically, the fluctuations are relatively small.) These fluctuations generally evolve according to well-behaved Markov processes that tend back towards the equilibrium values of the macroscopic variables on average. The fluctuation-dissipation theorem says that the assemblage's response to small external perturbations or forcings looks just like the dynamics of these spontaneous fluctuations. There are various ways of proving this, making use of more or less detailed physical considerations; many of them boil down to the assumption that equilibrium has to correspond to a stationary stochastic process. This in turn suggests that non-equilibrium assemblages in stationary states would have their own fluctuation-response relations, which is of special interest to me.