### Speaker

Rudolf Hilfer
(Universitaet Stuttgart)

### Description

Local equilibrium states change slowly in time because they
are almost stationary. As a consequence local equilibrium states
have to be related to local states that are time-invariant.
It has been argued in the literature that a proper mathematical
formulation of local equilibrium states must start from the class
of time-invariant measures for infinitely extended systems [1].
This presentation argues that the set of time-invariant measures
of infinite systems is too small [2]. A suitable extension are
states of bounded mean oscillation (BMO-states) that are also
close to time-invariant states. BMO-states are states for which
the expectation values of all observables are functions of
bounded mean oscillation in time. Results for long time scaling
limits of induced time flows on subsets of BMO-states then provide
the mathematical foundation for the local equilibrium concept.
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[1] H. Spohn, Large Scale Dynamics of Interacting Particles, 1991
[2] R. Hilfer, Analysis, 36, 49-64 (2016)

### Primary author

Rudolf Hilfer
(Universitaet Stuttgart)