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Mathematical Physics Seminar

On Typicality in Nonequilibrium Steady States

Lamberto Rondoni - University of Torino 

Location:  Hill 705
Date & time: Thursday, 28 February 2019 at 12:00PM - 1:00PM

Abstract:  Relaxation of macroscopic systems and response theory rest on a notion of typicality, according to which the behavior of single objects corresponds to a mean behavior computed over appropriate ensembles, because “almost all” objects share the same fate. In the case of non-dissipative dynamics and relaxation toward equilibrium states, “almost all” is usually taken in the sense of the Lebesgue measure: the initial microstates (single systems) that do not follow the ensemble constitute a set of vanishing phase space volume, and volume may be taken as a continuous counterpart of counting states. In the case of dissipative dynamics, states pile up on sets of zero volume, therefore "counting" turns problematic. We illustrate the dynamical condition called \(Omega T\)-mixing, that arises in some derivations of fluctuation theorems, as necessary and sufficient for relaxation of ensemble averages to steady state values. We then identify a variation of this condition, which refers to the volume of initial states, providing a notion of typicality for dissipative dynamics.


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