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Lamberto Rondoni

Dipartimento di Scienze Matematiche, Politecnico di Torino

Corso Duca degli Abruzzi 24, 10129 Torino, Italy

INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy

+39 011 090 7533 (office), +39 011 090 7599 (fax), +39 366 927 8093 (mobile)

http://calvino.polito.it/~rondoni

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Titolo: Nonequilibrium response, relaxation and the t-mixing condition

Abstract: In 1993 a relation was proposed by Evans, Cohen and Morriss, which has been

since known as Fluctuation Relation. This relation was initially intended to quantify

the relative probability of positive and negative energy dissipation rates in non-equilibrium

steady states. Later, it developed in many steady state as well transient relations.

The search for the minimal ingredients which allow such steady state fluctuation relations

to hold led to the formulation of the t-mixing condition. This condition, similarly to the

standard mixing condition, requires a certain decay of correlations, but different from

that concerning standard mixing. We illustrate how the notion of t-mixing arose in the

context of fluctuation relations, and we compare it with standard mixing properties.

Further, we note that besides yielding the fluctuation relations for dissipative, time

reversal invariant deterministic systems, without need to explicitly invoke special

properties for the phase space invariant measures, t-mixing leads to a number of other

results. We will discuss, in particular, those concerning relaxation to equilibrium or

non-equilibrium stationary states and those concerning a general Green-Kubo-like response

formula, which may be applied arbitrarily far from equilibrium to large as well as small

systems (with correspondingly different meanings).