Entropy production

Summary

Entropy production (or generation) is the amount of entropy which is produced during heat process to evaluate the efficiency of the process. Short history Entropy is produced in irreversible processes. The importance of avoiding irreversible processes (hence reducing the entropy production) was recognized as early as 1824 by Carnot. In 1865 Rudolf Clausius expanded his previous work from 1854 on the concept of "unkompensierte Verwandlungen" (uncompensated transformations), which, in our modern nomenclature, would be called the entropy production. In the same article in which he introduced the name entropy, Clausius gives the expression for the entropy production for a cyclical process in a closed system, which he denotes by N, in equation (71) which reads :N=S-S_0-\int\frac{dQ}{T}. Here S is the entropy in the final state and S0 the entropy in the initial state; S0-S is the entropy difference for the backwards part of the process. The integral is to be taken

Official source

https://en.wikipedia.org/wiki/Entropy_production

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Daniel Maria Busiello, Deepak Gupta

We consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links Herein, we first compute the statistical length and the thermodynamic cost function for transitions in the probability space, highlighting contributions from total, environmental, and resetting (unidirectional) entropy production. Then we derive the thermodynamic bound on the speed limit to connect two distributions separated by a finite time, showing the effect of the presence of unidirectional transitions. Uncertainty relationships can be found for the temporal first and second moments of the average resetting entropy production. We derive simple expressions in the limit of slow unidirectional transition rates. Finally, we present a refinement of the thermodynamic bound by means of an optimization procedure. We numerically investigate these results on systems that stochastically reset with constant and periodic resetting rate.

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Daniel Maria Busiello

Thermodynamic observables of mesoscopic systems can be expressed as integrated empirical currents. Their fluctuations are bound by thermodynamic uncertainty relations. We introduce the hyperaccurate current as the integrated empirical current with the least fluctuations in a given nonequilibrium system. For steady-state systems described by overdamped Langevin equations, we derive an equation for the hyperaccurate current by means of a variational principle. We show that the hyperaccurate current coincides with the entropy production if and only if the latter saturates the thermodynamic uncertainty relation, and it can be substantially more precise otherwise. The hyperaccurate current can be used to improve estimates of entropy production from experimental data.

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