Abstract:
Relaxation to equilibrium has a witness: the thermodynamic entropy
increases for thermally isolated systems to reach a maximal value
characterizing the typical outlook of equilibria. That fact gets translated
to the existence of Lyapunov functions (or H-functions) in physically
motivated differential equations. An important example is the ever
increasing H-functional in the theory of dilute gases following the Boltzmann
equation, but more generally the idea of entropic forces leads to
an understanding of close-to-equilibrium behavior. In this talk we ask
the question what remains of such monotonicity for open driven systems.
We present two types of candidates, one entropic, related to static
fluctuations and the other, called frenetic, related to dynamical fluctuation
theory. The main question is however to see what is their physical
-operational- meaning. Do these monotone quantities correspond to real
(nonequilibrium) thermodynamic forces? Do they essentially differ from
equilibrium forces? We give examples for interacting particle systems
(Markov processes) as studied also mathematically for studies of large
deviations in the context of probability theory.