## Non-Equilibrium Irreversible Thermodynamics and Uncertainty

by Tommy on 12/05/2017I’m always looking for new ways to look at non-equilibrium and irreversible thermodynamics.

https://arxiv.org/abs/1705.04027

A simple proof of the thermodynamic uncertainty relation, Changbong Hyeon and Wonseok Hwang (11 May 2017)

Using Brownian motion in periodic potential

V(x) tilted by a forcef, we prove the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipationq, and in order to limit the output fluctuation within a relative uncertainty ϵ, at least 2k_{B}T/ϵ^{2}of heat must be dissipated. We show that this bound is attained not only at near-equilibrium (f≪V′(x)) but also at far-from-equilibrium (f≫V′(x)), more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish. Our derivation of the uncertainty relation also recognizes a new bound of nonequilibrium dissipation that the variance of dissipated heat (σ^{2}q) increases with its mean (μq) and is greater than 2k_{B}Tμ_{q}.

Thermodynamic uncertainty certainly is a new way of looking at these subjects.

This paper is as insightful as it gets.

lifeform@charter.net
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