Related papers: Ensemble inequivalence in long-range quantum syste…
This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body…
A Hamiltonian model living in a bounded phase space and with long-range interactions is studied. It is shown, by analytical computations, that there exists an energy interval in which the microcanonical entropy is a decreasing convex…
For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and…
The inequivalence of thermodynamical ensembles related by a Legendre transformation is manifest in self-gravitating systems and in black hole thermodynamics. Using the Poincare's method of the linear series, we describe the mathematical…
A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number…
In statistical physics, the challenging combinatorial enumeration of the configurations of a system subject to hard constraints (microcanonical ensemble) is mapped to a mathematically easier calculation where the constraints are softened…
We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of…
The thermodynamics for a system with given temperature, density, and volume is described by the Canonical ensemble. The thermodynamics for a corresponding system with the same temperature, volume, and average density is described by the…
Equilibrium statistics of finite Hamiltonian systems is fundamentally described by the microcanonical ensemble (ME). Canonical, or grand-canonical partition functions are deduced from this by Laplace transform. Only in the thermodynamic…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
A great many observables seen in intermediate energy heavy ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble (energy and…
We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum…
Motivated by the anisotropic long-range nature of the interactions between cold dipolar atoms or molecules in an optical lattice, we study the anisotropic quantum Heisenberg model with Curie-Weiss-type long-range interactions. Absence of a…
We illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean-field Blume-Emery-Griffiths (BEG) model as a test model. The novel characterization takes effect at the level of the microcanonical and…
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…
The theory of small-system thermodynamics was originally developed to extend the laws of thermodynamics to length scales of nanometers. Here we review this "nanothermodynamics," and stress how it also applies to large systems that subdivide…
Statistical models based on canonical and grand canonical ensembles are extensively used to study intermediate energy heavy ion collisions. The underlying physical assumption behind canonical and grand canonical models is fundamentally…
Macroscopic thermodynamics, via the weak coupling approximation, assumes that the equi?librium properties of a system are not affected by interactions with its environment. However, this assumption may not hold for quantum systems, where…
We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and…
The equivalence of thermodynamic results in the canonical and the microcanonical ensembles has been questioned in some calculations for spin models with long-range interactions. We show that these claims of inequivalence are related to an…