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Register a new userComment on Fluctuation Theorem Uncertainty Relation and Thermodynamic Uncertainty Relations from Exchange Fluctuation Theorems
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Yunxin Zhang
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In recent letter [Phys.~Rev.~Lett {bf 123}, 110602 (2019)], Y.~Hasegawa and T.~V.~Vu derived a thermodynamic uncertainty relation. But the bound of their relation is loose. In this comment, through minor changes, an improved bound is obtained. This improved bound is the same as the one obtained in [Phys.~Rev.~Lett {bf 123}, 090604 (2019)] by A.~M.~Timpanaro {it et. al.}, but the derivation here is straightforward.
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Fluctuation theorems are fundamental results in non-equilibrium thermodynamics. Considering the fluctuation theorem with respect to the entropy production and an observable, we derive a new thermodynamic uncertainty relation which also applies to non-cyclic and time-reversal non-symmetric protocols.
Recent research has considered the stochastic thermodynamics of multiple interacting systems, representing the overall system as a Bayes net. I derive fluctuation theorems governing the entropy production (EP)of arbitrary sets of the systems in such a Bayes net. I also derive ``conditional fluctuation theorems, governing the distribution of EP in one set of systems conditioned on the EP of a different set of systems. I then derive thermodynamic uncertainty relations relating the EP of the overall system to the precisions of probability currents within the individual systems.
We introduce a new technique to bound the fluctuations exhibited by a physical system, based on the Euclidean geometry of the space of observables. Through a simple unifying argument, we derive a sweeping generalization of so-called Thermodynamic Uncertainty Relations (TURs). We not only strengthen the bounds but extend their realm of applicability and in many cases prove their optimality, without resorting to large deviation theory or information-theoretic techniques. In particular, we find the best TUR based on entropy production alone and also derive a novel bound for stationary Markov processes, which surpasses previous known bounds. Our results derive from the non-invariance of the system under a symmetry which can be other than time reversal and thus open a wide new spectrum of applications.
This is a comment to a letter by D. Mandal, K. Klymko and M. R. DeWeese published as Phys. Rev. Lett. 119, 258001 (2017).
The present work extends the well-known thermodynamic relation $C=beta ^{2}< delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest and a generalized thermostat, which we define in the course of the paper. The resulting identity $< delta beta delta {E}> =1+< delta {E^{2}}% > partial ^{2}S(E) /partial {E^{2}}$ can account for thermodynamic states with a negative heat capacity $C<0$; at the same time, it represents a thermodynamic fluctuation relation that imposes some restrictions on the determination of the microcanonical caloric curve $beta (E) =partial S(E) /partial E$. Finally, we comment briefly on the implications of the present result for the development of new Monte Carlo methods and an apparent analogy with quantum mechanics.
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