# Seminars & Colloquia Calendar

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.

THERE WILL BE A BROWN BAG LUNCH FROM 1-2PM

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