Related papers: Entropy as an adiabatic invariant
This paper is devoted to problems stated by Z. Zhou and F. Li in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map f and its topological entropy. The…
In recent papers, several authors have claimed that a definition of the thermodynamic entropy in terms of the logarithm of a volume in phase space, originally suggested by Gibbs, is the only valid definition. Arguing from the Gibbs entropy,…
This is a point-by-point response to a non-peer-reviewed document titled The Miscalibration of the Honeybee Odometer [arXiv:2405.12998], authored by L. Luebbert and L. Pachter, that was published on arXiv on 8 May 2024 and subsequently…
The connection between inequalities in additive combinatorics and analogous versions in terms of the entropy of random variables has been extensively explored over the past few years. This paper extends a device introduced by Ruzsa in his…
In our paper arXiv:1310.6289, we stated that acylindrical hyperbolicity of a group is invariant under commensurability up to finite kernels. Unfortunately, the proof of this fact contained a gap. The goal of this erratum is to point out the…
Adiabaticity is a cornerstone of many promising approaches to quantum control, computing, and simulation. In practice, however, there is always a trade-off. Although the deleterious effects of noise can be diminished by running a control…
In this article it will be introduced a new theorem, can be considered a generalization of Hellmann-Feynman theorem[1]. The latter used in conjunction with the quantization of the free energy[2] of a quantum system allows to derive…
The Kelvin-Planck statement of the Second Law of Thermodynamics is a stricture on the nature of heat receipt by any body suffering a cyclic process. It makes no mention of temperature or of entropy. Beginning with a Kelvin-Planck statement…
I show that for two inverse temperatures $\beta_1$ and $\beta_2$, the von Neumann entropy $S(\rho_\beta)$ of the Gibbs state $\rho_\beta$ for a given Hamiltonian $H$ satisfies $S(\rho_{\beta_1}) \geq S(\rho_{\beta_2}) \iff \beta_{1} \leq…
In this paper, we present an invariant perturbation theory of the adiabatic process based on the concepts of U(1)-invariant adiabatic orbit and U(1)-invariant adiabatic expansion. As its application, we propose and discuss new adiabatic…
The Boltzmann-Gibbs celebrated entropy $S_{BG}=-k\sum_ip_i \ln p_i$ is {\it concave} (with regard to all probability distributions $\{p_i\}$) and {\it stable} (under arbitrarily small deformations of any given probability distribution). It…
The partial adiabatic search algorithm was introduced in [A. Tulsi, Phys. Rev. A 80, 052328 (2009)] as a modification of the usual adiabatic algorithm for quantum search with the idea that most of the interesting computation only happens…
The weighted forms of generalized survival and failure entropies of order ($\alpha,\beta$) are proposed and some properties are obtained. We further propose the dynamic versions of weighted generalized survival and failures entropies and…
The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the…
We reveal a correspondence between temperature and integrability-breaking in classical and quantum many-body systems through the lens of geometry and adiabatic transformations. Decreasing the temperature, obtained in a standard way through…
A considerable body of experimental and theoretical work claims the existence of negative absolute temperatures in spin systems and ultra-cold quantum gases. Here, we clarify that such findings can be attributed to the use of a popular yet…
A generalization of the Gibbs entropy postulate is proposed based on the BBGKY hierarchy as the nonequilibrium entropy for a system of N interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that…
We introduce an ergotropy-based formulation of quantum thermodynamics, which provides a strong connection between average heat and von Neumann entropy. By adopting this formulation, we can reinterpret the infinitesimal average heat in terms…
We critically examine the applicability of the effective potential within dynamical situations and find, in short, that the answer is negative. An important caveat of the use of an effective potential in dynamical equations of motion is an…
The physical impossibility of heat transfer under isothermal conditions implies that the classical expression for the entropy of the ideal gas may not be compatible with the internal energy of the gas itself. A corrected expression of the…