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We discuss the validity of recent results in [Phys. Rev. Lett. 125, 125501 (2020)] on an universal relation between the heat capacity and dispersions of collective excitations in liquids.
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We show, that the theoretical expression for the dispersion of collective excitations reported in [Phys. Rev. B {bf 103}, 099901 (2021)], at variance with what was claimed in the paper, does not account for the energy fluctuations and does not tend in the long-wavelegth limit to the correct hydrodynamic dispersion law.
We show that the presented in Phys.Rev.B, v.101, 214312 (2020) theoretical expressions for longitudinal current spectral function $C^L(k,omega)$ and dispersion of collective excitations are not correct. Indeed, they are not compatible with the continuum limit and $C^L(k,omegato 0)$ contradicts the continuity equation.
We provide some analytical tests of the density of states estimation from the localization landscape approach of Ref. [Phys. Rev. Lett. 116, 056602 (2016)]. We consider two different solvable models for which we obtain the distribution of the landscape function and argue that the precise spectral singularities are not reproduced by the estimation of the landscape approach.
Heat engines used to output useful work have important practical significance, which, in general, operate between heat baths of infinite size and constant temperature. In this paper we study the efficiency of a heat engine operating between two finite-size heat sources with initial temperature differences. The total output work of such heat engine is limited due to the finite heat capacity of the sources. We investigate the effects of different heat capacity characteristics of the sources on the heat engines efficiency at maximum work (EMW) in the quasi-static limit. In addition, we study the efficiency of the engine working in finite-time with maximum power of each cycle is achieved and find the efficiency follows a simple universality as $eta=eta_{mathrm{C}}/4+Oleft(eta_{mathrm{C}}^{2}right)$. Remarkably, when the heat capacity of the heat source is negative, such as the black holes, we show that the heat engine efficiency during the operation can surpass the Carnot efficiency determined by the initial temperature of the heat sources. It is further argued that the heat engine between two black holes with vanishing initial temperature difference can be driven by the energy fluctuation. The corresponding EMW is proved to be $eta_{mathrm{EMW}}=2-sqrt{2}$, which is two time of the maximum energy release rate $mu=left(2-sqrt{2}right)/2approx0.29$ of two black hole emerging process obtained by S. W. Hawking.
By using very general arguments, we show that the entropy loss conjecture at the glass transition violates the second law of thermodynamics and must be rejected.
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