Related papers: Seeing maximum entropy from the principle of virtu…
Depending on context, the term entropy is used for a thermodynamic quantity, a~measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in…
We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system's properties and the entropy. System's constraints other than fixed number…
A statistical-mechanical investigation is performed on Rayleigh-B\'enard convection of a dilute classical gas starting from the Boltzmann equation. We first present a microscopic derivation of basic hydrodynamic equations and an expression…
Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In…
We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…
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 examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
Numerical methods for the description of nonequilibrium many-particle quantum systems such as equation of motion techniques often cannot compute the full statistics of observables but only moments of it, such as mean, variance and…
In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
We develop a new theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of non-equilibrium statistical mechanics. The general form of the many-body density matrix is…
G\'acs' coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables…
We show that the law of energy conservation with the fact of matter stability imply the existence of energy complementary to that given by the function of states of interacting systems and treated, with the environment, the function of…
The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is addressed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for both…
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method…
We present a maximum entropy approach to analyze the internal dynamics of a small system in contact with a large bath e.g. a solute-solvent system. For the small solute, the fluctuations around the mean values of observables are not…
Many physicists think that the maximum entropy formalism is a straightforward application of Bayesian statistical ideas to statistical mechanics. Some even say that statistical mechanics is just the general Bayesian logic of inductive…
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of…
Originally formulated for macroscopic machines, the laws of thermodynamics were recently shown to hold for quantum systems coupled to ideal sources of work (external classical fields) and heat (systems at equilibrium). Ongoing efforts have…