102.
We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems,
which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation
yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium
steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state
are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation
is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations
in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the
resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities.
The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression
factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been
considered previously, and show how they are described in the context of this work.
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