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The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by…
We show that, when we study the coexistence of general relativity with thermodynamics, some physical properties that are usually thought of as holographic and lying in the domain of quantum gravity can actually be accessed even at the…
Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up…
We investigate the thermodynamic properties of a Restricted Boltzmann Machine (RBM), a simple energy-based generative model used in the context of unsupervised learning. Assuming the information content of this model to be mainly reflected…
The onset of thermalization in a closed finite system of randomly interacting bosons, at the level of a single eigenstate, is discussed. The main interest is in the emergence of the Bose-Einstein distribution of single-particle occupation…
This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down…
We consider the statistical mechanics of a small gaseous system subject to a constant external field. As is well known, in the canonical ensemble the system i) obeys a barometric formula for the density profile and ii) the kinetic…
Mixed state ensembles such as the Bures-Hall and Hilbert-Schmidt measure are probability distributions that characterise the statistical properties of random density matrices and can be used to determine the typical features of mixed…
A simple procedure for obtaining superpositions of macroscopically distinct states is proposed and analyzed. We find that a thermal equilibrium state can be converted into such a state when a single global measurement of a macroscopic…
Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states.…
Most elemental metals under ambient conditions adopt simple structures such as BCC, FCC and HCP in specific groupings across the Periodic Table, and on compression, many of these elements undergo transitions to surprisingly complex…
We consider a system of particles subjected to a uniform external force E and undergoing random collisions with "virtual" fixed obstacles, as in the Drude model of conductivity. The system is maintained in a nonequilibrium stationary state…
We use the work done on and the heat removed from a system to maintain it in a nonequilibrium steady state for a thermodynamic-like description of such a system as well as of its fluctuations. Based on a generalized Onsager-Machlup theory…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann-Planck's principle,…
This work describes the statistics for the occupation numbers of quantum levels in a large isolated quantum system, where all possible superpositions of eigenstates are allowed, provided all these superpositions have the same fixed energy.…
The eigenstate thermalization hypothesis provides a framework for understanding thermalization in isolated quantum many-body systems by characterizing statistical properties of local observables in energy eigenstates. Here we demonstrate…
This paper gives a concise, mathematically rigorous description of phenomenological equilibrium thermodynamics for single-phase systems in the absence of chemical reactions and external forces. The present approach is similar to that of…
Based on statistical mechanics, a macroscopically homogeneous system, i.e., a single phase in the present context, is composed of many independent configurations that the system embraces. The macroscopical properties of the system are…
We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit…