Related papers: Generalized canonical ensembles and ensemble equiv…
In this chapter, we present a straightforward geometrical argument that in a certain way recalls us the equivalence between the canonical and the microcanonical ensembles in the thermodynamic limit for the particular context of physical…
The Blume-Capel model with infinite-range interactions presents analytical solutions in both canonical and microcanonical ensembles and therefore, its phase diagram is known in both ensembles. This model exhibits nonequivalent solutions and…
A pedagogical approach for deriving the statistical mechanical partition function, in a manner that emphasizes the key role of entropy in connecting the microscopic states to thermodynamics, is introduced. The connections between the…
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 prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it…
The Gaussian $\beta$-ensemble (G$\beta$E) is a fundamental model in random matrix theory. In this paper, we provide a comprehensive asymptotic description of the characteristic polynomial of the G$\beta$E anywhere in the bulk of the…
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…
The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is argued to be determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of…
The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' $q-$average of physical quantities, the sum $\sum…
It is well known that a system, S, weakly coupled to a heat bath, B, is described by the canonical ensemble when the composite, S+B, is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true both for…
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is…
This paper develops a gravitational-thermodynamic interpretation of two ensemble structures with singular behavior, denoted as canonical ensemble A and grand canonical ensemble B. Ensemble A is modeled as a stellar-type system in which…
For substitutional crystalline solids typically referred to classical discrete system under constant composition, macroscopic structure in thermodynamically equilibrium state can be typically obtained through canonical average, where a set…
We discuss equivalent representations of the collective/bosonic Hamiltonian in the form of Taylor expansion over collective coordinate and momentum. Different expansions are equivalent if they are related by a transformation of collective…
In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is…
In this work we generalize and combine Gibbs and von Neumann approaches to build, for the first time, a rigorous definition of entropy for hybrid quantum-classical systems. The resulting function coincides with the two cases above when the…
This study shows that the generalized Boltzmann distribution is the only distribution mathematically consistent with thermodynamics when the system is described by an ensemble of a certain mathematical form. This mathematical form is very…
Microcanonical description is characterized by the presence of an internal symmetry closely related with the dynamical origin of this ensemble: the reparametrization invariance. Such symmetry possibilities the development of a non…
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…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…