Abstract
We review the physical meaning and mathematical implementation of the condition of local detailed balance for a class of nonequilibrium mesoscopic processes. A central concept is that of fluctuating entropy flux for which the steady average gives the mean entropy production rate. We repeat how local detailed balance is essentially equivalent to the widely discussed fluctuation relations for that entropy flux and hence is at most ``only half of the story.''
Highlights
How to construct a statistical mechanical model for nonequilibrium processes that leads naturally to the existence of a stationary state? That question makes the opening line of the paper by Bergmann and Lebowitz (1955) proposing a new modeling framework for the description of irreversible processes [1, 2]
The resulting stochastic models and identification of currents and entropy flows followed the procedure of what is called the condition of local detailed balance (LDB)
When modeling an open system weakly coupled to equilibrium baths which are well-separated, it makes good sense, and time-symmetry requires, to impose LDB
Summary
How to construct a statistical mechanical model for nonequilibrium processes that leads naturally to the existence of a stationary state? That question makes the opening line of the paper by Bergmann and Lebowitz (1955) proposing a new modeling framework for the description of irreversible processes [1, 2]. How to construct a statistical mechanical model for nonequilibrium processes that leads naturally to the existence of a stationary state? The resulting stochastic models and identification of currents and entropy flows followed the procedure of what is called the condition of local detailed balance (LDB). When modeling an open system weakly coupled to equilibrium baths which are well-separated, it makes good sense, and time-symmetry requires, to impose LDB. It has been used as a modeling guide, especially when introducing the problem of current fluctuations; see e.g. Section 2 in [5]. At best LDB determines only half of the dynamical ensemble for nonequilibria; the rest is subject to the so called frenetic contribution [9]
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