Gibbs and non-Gibbs measures in space and time

Frank Redig

Date(s) : 03/02/2012   iCal
10 h 00 min - 12 h 00 min

Gibbs measures are the mathematical formalization of Boltzmann-Gibbs distributions and describe equilibrium states of extended systems in statistical mechanics. If one starts a system in equilibrium and subjects it to a dynamics, modelling e.g. heating or cooling, a natural question is whether some “effective” interaction describes the transient non-equilibrium states that the systems goes through. Starting with the simplest example of a lattice system with Ising spins, we show that quite generically, if one heats up a low-temperature system, the Gibbs property will be lost (and sometimes recovered) in the course of time, i.e., a reasonable effective interaction does typically not exist for all times. We show how this can be related to large deviation properties of Markov processes conditioned to arrive at an “exceptional” state in the future. Depending on how far in the future the conditioning occurs, optimal trajectories can be unique or non-unique.
Based on joint work with A. van Enter, R. Fernandez, F. den Hollander.

Frank Redig

FRUMAM, St Charles


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