In a recent perspective article, Horowitz and Gingrich discuss thermodynamic uncertainty relations that have been derived using "stochastic thermodynamics", a theory based on a hypothesis known as local detailed balance. The authors examined the foundations of this theory in their "Box 1: A brief primer on local detailed balance and stochastic thermodynamics", where a kinetic scheme for transport of particles between two reservoirs is presented. Horowitz and Gingrich arrive at a relationship between the probability to cycle through the states in one order vs. the probability to cycle in the reverse order. This relation bears on the extremely important question of what governs directionality when a system is driven away from equilibrium by contact with multiple reservoirs that are not in equilibrium with one another. In the original version of their paper the relation given for this ratio was obviously wrong and contrary to the second law of thermodynamics. Based on our private communications and on the recent paper authored by my colleagues and myself, Horowitz and Gingrich accepted the necessity of correcting the error in their Box 1. Unfortunately, in making the correction, the authors introduced an equally serious, if less transparent, mistake, and continue to base their theory on the thermodynamically impossible idea that transitions are mediated by only one of the two reservoirs. In this comment we illustrate how the principle of microscopic reversibility reveals that the true origin of directional cycling amongst a network of states is kinetic asymmetry. This understanding is important in guiding synthesis of molecular machines and other devices designed to exploit transport or catalysis to drive non-equilibrium processes.
An extension of the thermodynamic uncertainty relation (TUR) to time-delayed Langevin systems has been recently proposed by T. V. Vu and Y. Hasegawa (arXiv:1809.06610v2). Here we show that the derivation is erroneous.
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.
In a recent paper [P. Strasberg and M. Esposito, Phys. Rev. E {\bf 101}, 050101(R) (2020)] an attempt is presented to formulate the nonequilibrium thermodynamics of an open system in terms of the Hamiltonian of mean force. The purpose of the present comment is to clarify severe restrictions of this approach and also to stress that recently noted ambiguities [P. Talkner and P. Hänggi, Phys. Rev. E {\bf 94}, 022143 (2016)] of fluctuating thermodynamic potentials cannot be removed in the suggested way.
B. Amorim et al., (B.Amorim, R.Roldan, E.Cappelluti, A.Fasolino, F.Guinea, M.I.Katsnelson, Phys. Rev. B, v. 89, 224307 (2014)) reported the theoretical investigation of quantum crystalline membranes. In this comment we dismiss validity of their calculations based on a "natural" estimation of the ultra-violet (UV) divergent contributions into correlation functions. We claim that such calculations may not be performed correctly within the long-scale theory.
Recently, Gross claims that Boltzmann entropy $S=k\ln W$ is valid for any system at equilibrium, so that Tsallis entropy is useless in this case. I comment on some arguments forwarded to reach this conclusion and argue that the additive energy formalism of nonextensive statistics is not appropriate for the fundamental study of the theory for nonadditive systems.
Bento \textit{et al.} [Phys. Rev. E 91, 022105 (2015)] state that the Tsallis entropy violates the third law of thermodynamics for $q \leq 0$ and $0<q<1$. We show that their results are valid only for $q \geq 1$, since there is no distribution maximizing the Tsallis entropy for the intervals $q \leq 0$ and $0<q<1$ compatible with the system energy expression.
We comment on letter ``Is Tsallis Thermodynamics Nonextensive?'' by E. Vives and A. Planes [Phys. Rev. Lett. 88, 020601 (2002) cond-mat/0106428]. It is pointed out that the Euler and Gibbs-Duhem equations derived in the letter can serve to justify an appropriate form for the Lagrange parameters controlling thermal equilibrium, without need of any change of variables. This leads to a framework for Tsallis Thermodynamics which is free from recent criticisms raised by Nauenberg [Phys. Rev. E 67, 036114 (2003) cond-mat/0210561] and Gross [Physica (Amsterdam) 305, 99 (2002) cond-mat/0106496]. This …
We refute the criticism expressed in a comment by P. Talkner and P. Hänggi [Phys. Rev. E 102, 066101 (2020)] on our paper Phys. Rev. E 101, 050101(R) (2020). We first make clear that our paper is free of any technical mistakes. We then defend the statements of our manuscript which were claimed to be taken out of context. Finally, we give clear arguments showing that the basic concepts we rely on are meaningful and have a deep rational.
The experimental verification of the fluctuation theorem by Wang et al. is explained in terms of a simple Langevin dynamics. This implies that the entropy consuming trajectories found by Wang et al. are fluctuations generated by a random force and do not violate the second law.
In a recent letter [PRL 95, 140601 (2005)], P. Grassberger addresses the very interesting issue of the applicability of q-statistics to the renowned Feigenbaum attractor. However several points are not in line with our current knowledge, nor are the interpretations that he advances.
The paper by Malek Mansour and Garcia [Phys. Rev. E 101, 052135 (2020)] is shown to be based on misconceptions in the stochastic formulation of chemical thermodynamics in reactive systems. Their erroneous claims, asserting that entropy production cannot be correctly evaluated using path probabilities whenever the reactive system involves more than one elementary reaction leading to the same composition changes, are refuted.
It is shown that there is bi-stability in a two dimensional system consisting of non interacting magnetic nanoparticles with equal uniaxial anisotropies. It is also shown that bi-stability still remains in three dimensions. The only consideration is that the applied magnetic field has to be perpendicular to the anisotropy axis.
It is shown that the argument presented in astro-ph/0307318 against the proof that the diluted limit of a self-gravitating system is ill behaved [Nucl. Phys. B668, 409 (2003) (astro-ph/0303301)] is misleading.
In this note, we reply to the comment made by E.I.Kats and V.V.Lebedev [arXiv:1407.4298] on our recent work "Thermodynamics of quantum crystalline membranes" [Phys. Rev. B 89, 224307 (2014)]. Kats and Lebedev question the validity of the calculation presented in our work, in particular on the use of a Debye momentum as a ultra-violet regulator for the theory. We address and counter argue the criticisms made by Kats and Lebedev to our work.
We comment that the model proposed in Phys. Rev. Lett. 108, 120603 (2012) violates the dynamical version of the third law of thermodynamics. We discuses the different formulations of the third law of thermodynamics and suggest a possible reason for the violation.
It is shown that the equations for pressure, entropy and the isochoric heat capacity obtained by using generalization of the equilibrium thermodynamics in fractional derivatives in the paper mentioned above are approximate, the comparison of the equations with the experimental (tabulated) data for Neon and Argon made in the paper is incorrect, and the conclusions of the paper made on the basis of the comparison could be incorrect. The conditions for validity of the equations are established. It is also established that the question about a physical sense of the exponent of the derivative of a …
In this note it is shown that in his ``Comments'', Tsallis did not point out any flaws in the main criticism of my paper, namely, that the nonextensive q-entropy formalism fails to satisfy the zeroth law of thermodynamics. Details are also given of a rigorous thermodynamic proof which demonstrates that, contrary to Tsallis's assertion, the application of a nonextensive formalism to black-body radiation does not lead to the well known $T^4$ Stefan-Boltzman law.
It is shown that the existence of single critical point of the fluid described by van der Waals equation of state is not the hypothesis and it is the consequence of the thermodynamic conditions of liquid-vapor phase equilibrium. It is also shown that the thermodynamic conditions of liquid-vapor phase equilibrium of the fluid give equalities to zero of first and second partial derivatives at constant temperature of pressure with respect to volume at critical point which are usual conditions of existence of critical point.
In a recent Letter [EPL, 118 (2017) 40003], Polettini and Esposito claimed that it is theoretically possible for a thermodynamic machine to achieve Carnot efficiency at divergent power output through the use of infinitely-fast processes. It appears however that this assertion is misleading as it is not supported by their derivations as demonstrated below. In this Comment, we first show that there is a confusion regarding the notion of optimal efficiency. We then analyze the quantum dot engine described in Ref. [EPL, 118 (2017) 40003] and demonstrate that Carnot efficiency is recovered only for…
J. E. Hirsch [EPL 130 (2020) 17006] claimed an inconsistency between thermodynamics and the theory of superconductivity. We argue that he overlooked a crucial term which determines the supercurrent dynamics and ensures energy conservation by providing an internal energy source for the Joule heating. Thermodynamic consistency is restored by restoring energy conservation. The correct dynamics is given by Maxwell's equations in the superconductor.
In Phys. Rev. Lett. 128, 200501 (2022) the authors consider the thermodynamic cost of quantum metrology. One of the main results is $\mathcal{S} \geq \log(2) \| h_λ\|^{-2} F_Q [ψ_λ]$, which purports to relate the Shannon entropy $\mathcal{S}$ of an optimal measurement (i.e., in the basis of the symmetric logarithmic derivative) to the quantum Fisher information $F_Q$ of the pure state $|ψ_λ\rangle$. However, we show that in the setting considered by the authors we have $\mathcal{S} = \log(2)$ and $\| h_λ\|^{2} = \max_{ψ_λ} F_Q[ψ_λ]$, so that their inequality reduces to the trivial inequality $…
In their comment to the paper ``Theory of the evaporation/condensation transition of equilibrium droplets in finite volumes'' [Physica A, 319, 99 (2003)], Biskup et al. claim that in finite systems at fixed density ``the physical significance of the conjugate thermodynamic variable is of dubious value''. This claim is critically discussed.
It is mentioned that anyon thermodynamic potential $Q(α, N)$ could not be factorized in terms characteristic of the ideal boson $α=0$ and fermion $α=1$ gases by the relation $Q(α, N) = (1-α) Q(0, N_b)+ αQ(1, N_f)$ in which $N=N_f +N_b$, that claimed in Phys. Rev. Lett. 78, 3233 (1997). Our analyses indicate that the thermodynamic quantities of anyon gas may be factorized as $Q(α) = αQ(1) + (1-α) Q(0)$ only in the two-dimension system.
In Phys. Rev. Lett. 67, 937 (1991) [1], Haldane introduced the fruitful concept of fractional exclusion statistics (FES). One of the most influential papers in which the thermodynamics of FES systems was deduced is Y.-S. Wu, Phys. Rev. Lett. 73, 922 (1994). Unfortunately, some important, but eventually subtle, properties of the exclusion statistics parameters were overlooked in the original paper [1] and in all the papers after that, including [2]. This omission makes the thermodynamics of FES systems inconsistent when mutual exclusion statistics is manifesting in the system. By this Comment I…
We comment the recent manuscript by Vollmayr-Lee and Luijten [cond-mat/0009031] focusing on classical systems with nonintegrable interactions. The authors claim that they have proved that Boltzmann-Gibbs statistics suffices for describing the system in thermal equilibrium. We show that this statement is a misleading oversimplification since it only applies for the $\lim_{N \to \infty} \lim_{t \to \infty}$ ordering, but certainly not for the $\lim_{t \to \infty} \lim_{N \to \infty}$ one. The latter can even be the {\it unique} physically meaningful situation for thermodynamically large systems.
We point out the erroneous reasoning and disprove the conclusions contained in a recent preprint by A. H. Bougourzi (arxiv:1402.3855v1) concerning the spin structure factor of the Heisenberg model at zero field in the thermodynamic limit, as calculated using the vertex operator approach.
Huerta et al. [Phys. Rev. Research 2, 033351 (2020)] report a power-law decay of positional order in numerical simulations of hard disks confined within hard parallel walls, which they interpret as a Kosterlitz-Thouless-type caging-uncaging transition. The proposed existence of such a transition in a quasi-one-dimensional (q1D) system, however, contradicts long-held physical expectations. To clarify if the proposed ordering persists in the thermodynamic limit, we introduce an exact transfer matrix approach to expeditiously generate equilibrium configurations for systems of arbitrary size. The …
We present a simple biophysical example that invalidates the main conclusion of "Nat. Commun. 10, 3542 (2019)". Moreover, we explain that systems with one or more hidden states between at least one pair of observed states that give rise to non-instantaneous transition paths between these states also invalidate the main conclusion of the aforementioned work. This provides a flexible roadmap for constructing counterexamples. We hope for this comment to raise awareness of possibly hidden transition paths and of the importance of considering the microscopic origin of emerging non-Markovian (or Mar…
We comment on recent numerical experiments by G.Hed and E.Domany [cond-mat/0608535v2] on the quenched equilibrium state of the Edwards-Anderson spin glass model. The rigorous proof of overlap identities related to replica equivalence shows that the observed violations of those identities on finite size systems must vanish in the thermodynamic limit. See also the successive version cond-mat/0608535v4
In a recent letter [Phys. Rev. Lett. 89, 156603 (2002); cond-mat/0201300], Alvarez and Gros have numerically analyzed the Drude weight for thermal transport in spin ladders and frustrated chains of up to 14 sites and have proposed that it remains finite in the thermodynamic limit. In this comment, we argue that this conclusion cannot be sustained if the finite-size analysis is taken to larger system sizes.
Recently, Brevik et al. [Phys. Rev. E 71, 056101 (2005)] adduced arguments against the traditional approach to the thermal Casimir force between real metals and in favor of one of the alternative approaches. The latter assumes zero contribution from the transverse electric mode at zero frequency in qualitative disagreement with unity as given by the thermal quantum field theory for ideal metals. Those authors claim that their approach is consistent with experiments as well as with thermodynamics. We demonstrate that these conclusions are incorrect. We show specifically that their results are c…
Recently Allahverdyan and Nieuwenhuizen (cond-mat/0006404) argued that the second law of thermodynamics may be violated in a quantum system as a "consequence of quantum coherence in the presence of the slightly off-equilibrium nature of the bath." By using a standard result about relative entropy, we prove rigorously that the second law is never violated (and, in particular, a perpetual motion of the second kind can never be realized) in quantum systems no matter how strong ``quantum coherence'' is or no matter how far one goes from equilibrium.
In a recent paper [Entropy 2020, 22(1), 17] C. Tsallis states that entropy -- as in Shannon's or Kullback-Leiber's definitions -- is inadequate to interpret black hole entropy and suggests that a new non-additive functional should take the role of entropy. Here we counter argue by explaining the important distinction between the properties of extensivity and additivity, the latter is fundamental for entropy while the former is a property of particular thermodynamical systems that is not expected on black holes. We also point out other debatable statements in his analysis of black hole entropy.
We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally described by the (non-additive) Tsallis entropy. We point out the form of the modified Legendre transform that should be used, instead, in the non-additive thermodynamics induced by the Tsallis entropy. We comment on more general implications of this proposal for the thermodynamics of "complex systems".
