Related papers: Relation between Boltzmann and Gibbs entropy and e…
In order to undestand how the complex concept of entropy emerged,we propose a trip towards the past reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since the Gibbs's work is not very well known, we present a…
We derive an exact expression of the response function to an infinitesimal magnetic field for the Ising-Glauber model with arbitrary exchange couplings.nThe result is expressed in terms of thermodynamic averages and does not depend on…
We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…
The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the…
In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by…
We expand upon a natural analogy between Bayesian statistics and statistical physics in which sample size corresponds to inverse temperature. This analogy motivates the definition of two novel statistical quantities: a learning capacity and…
We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can…
We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage…
The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of…
For a quantum system in a macroscopically large volume $V$, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system $v\ll V$ is almost surely totally mixed. We show…
A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy $S_{BG}$ and its associated exponential BG factor. Frequent…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…
This paper studies the Gibbs measure of an interacting particle system with a general interaction kernel at various temperature regimes. We are particularly interested in fine features of the convergence to the mean-field density as the…
We suggest a certain statistical interpretation for the entropy produced in driven thermodynamic processes. The exponential function of half irreversible entropy re-weights the probability of the standard Ornstein-Uhlenbeck-type…
The possible distinction between inanimate and living matter has been of interest to humanity since thousands of years. Clearly, such a rich question can not be answered in a single manner, and a plethora of approaches naturally do exist.…
There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability…
Boltzmann defined the entropy of a macroscopic system in a macrostate $M$ as the $\log$ of the volume of phase space (number of microstates) corresponding to $M$. This agrees with the thermodynamic entropy of Clausius when $M$ specifies the…