Title: Fluctuation Relations in Small Systems – Exact Results from the Deterministic Approach

Abstract: Many of the nano-scale systems at the cutting edge of contemporary
theoretical or experimental investigation are not at equilibrium.  This
has proven a strong motivation in the development of nonequilibrium
theories relevant on such scales.  One intensely researched area is that
of the Fluctuation Relations, which describe the fluctuations of
nonequilibrium system observables.  The focus in recent years has been
on the disambiguation of results that ostensibly appear the same, yet
differ in crucial (but subtle) ways.  This is particularly the case for
results that pertain to the steady state, which are highly relevant for
small systems.  Our aim here is to elaborate on these recent efforts,
particularly in the context of small systems.  In particular, we
consider the relevance of the connection between the dynamics and the
initial distribution, and we focus on the passage from the transient
results to results for the steady state.  By undertaking a rigorous
mathematical approach, one can shed light on some of the key physical
intuitions, such as a particular form of correlations decay, that have
played an important role in the development of these Relations

Keywords: Response theory, molecular dynamics, Generalized Liouville Equation, t-mixing property