Related papers: Reconnecting statistical physics and combinatorics…
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…
We consider a paradigmatic model describing the one-dimensional motion of $N$ rotators coupled through a mean-field interaction, and subject to the perturbation of an external magnetic field. The latter is shown to significantly alter the…
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…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
We propose a description of pairing properties in finite systems within the canonical and microcanonical ensembles. The approach is derived by solving the BCS and self-consistent quasiparticle random-phase approximation with the…
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…
We present a full treatment of the microcanonical ensemble of the ideal hadron-resonance gas in a quantum-mechanical framework which is appropriate for the statistical model of hadronization. By using a suitable transition operator for…
Ab initio path integral Monte Carlo (PIMC) simulations constitute the gold standard for the estimation of a broad range of equilibrium properties of a host of interacting quantum many-body systems spanning conditions from ultracold atoms to…
The unconstrained ensemble describes completely open systems whose control parameters are chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of…
The dynamical justifications which lie at the basis of an effective Statistical Mechanics for self gravitating systems are formulated, analyzing some among the well known obstacles thought to prevent a rigorous Statistical treatment. It is…
We introduce and analyse ensembles of 2-regular random graphs with a tuneable distribution of short cycles. The phenomenology of these graphs depends critically on the scaling of the ensembles' control parameters relative to the number of…
The canonical statistics describes the statistical properties of an open system by assuming its coupling with the heat bath infinitesimal in comparison with the total energy in thermodynamic limit. In this paper, we generally derive a…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce the thermodynamic and structural properties. The objective is to develop a means for exploiting strong coupling classical methods (e.g.,…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
The (non-)equivalence of canonical and microcanonical ensembles is a fundamental question in statistical physics, concerning whether the use of soft and hard constraints in the maximum-entropy construction leads to the same description of a…
We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
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…
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…
For classical discrete systems under constant composition, a set of microscopic state dominantly contributing to thermodynamically equilibrium structure should depend on temperature and energy through Boltzmann factor, exp(-bE). Despite…