Related papers: Nonconcave entropies from generalized canonical en…
Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and…
Two simple spin models are studied to show that the microcanonical entropy can be a non-concave function of the energy, and that the microcanonical and canonical ensembles can give non-equivalent descriptions of the same system in the…
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…
We derive the thermodynamic entropy of the mean field $\phi^{6}$ spin model in the framework of the micro-canonical ensemble as a function of the energy and magnetization. Using the theory of large deviations and Rugh's micro-canonical…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In…
The anisotropic quantum Heisenberg model with Curie-Weiss-type interactions is studied analytically in several variants of the microcanonical ensemble. (Non)equivalence of microcanonical and canonical ensembles is investigated by studying…
Using the theory of large deviations, we analyze the phase transition structure of the Curie-Weiss-Potts spin model, which is a mean-field approximation to the Potts model. This analysis is carried out both for the canonical ensemble and…
Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called…
We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by…
We discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as Legendre-Fenchel transforms of functions analogous to free energy functions. We show that the Legendre-Fenchel transform of a free energy…
This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor $e^{-\beta H}$ of the…
Generalized entropy, that has been recently proposed, puts all the known and apparently different entropies like The Tsallis, the R\'{e}nyi, the Barrow, the Kaniadakis, the Sharma-Mittal and the loop quantum gravity entropy within a single…
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 microcanonical entropy s(e,m) as a function of the energy e and the magnetization m is computed analytically for the anisotropic quantum Heisenberg model with Curie-Weiss-type interactions. The result shows a number of interesting…
Shortened abstract: Microcanonical equilibrium macrostates are characterized as the solutions of a constrained minimization problem, while canonical equilibrium macrostates are characterized as the solutions of a related, unconstrained…
Given physical systems, counting rule for their statistical mechanical descriptions need not be unique, in general. It is shown that this nonuniqueness leads to the existence of various canonical ensemble theories which equally arise from…
We propose a method for the numerical computation of microcanonical expectation values--i.e. averages over energy eigenstates with the same eigenvalue-without any prior knowledge about the spectrum of the Hamiltonian. This is accomplished…
Two recently proposed expressions for the computation of the entropy in the microcanonical ensemble are compared, and their equivalence is proved. These expressions are valid for a certain class of statistical mechanics systems, that can be…
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 non-extensive statistical mechanics has been used to describe a variety of complex systems. The maximization of entropy, often used to introduce the non-extensive statistical mechanics, is a formal procedure and does not easily leads to…