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Non-equilibrium states of a thermodynamic statistical system are investigated using the thermodynamic parameter of the system lifetime, first-passage time, the time before degeneration of the system under influence of fluctuations.…
The hyperensembles, introduced by Crooks in a context of non-equilibrium statistical physics, are considered here as a tool for systems in equilibrium. Simple examples like the ideal gas, the mean-field model, and the Ising interaction on…
Ensemble inequivalence occurs when a systems thermodynamic properties vary depending on the statistical ensemble used to describe it. This phenomenon is known to happen in systems with long-range interactions and has been observed in many…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if 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…
Equilibrium phase transitions usually emerge from the microscopic behavior of many-body systems and are associated to interesting phenomena such as the generation of long-range order and spontaneous symmetry breaking. They can be defined…
To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is…
Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and…
The use of the isoconfigurational ensemble to explore structure-dynamic correlations in supercooled liquids is examined. The statistical error of the dynamic propensity and its spatial distribution are determined. The authors present the…
Ensemble forecasting is a technique devised to palliate sensitivity to initial conditions in nonlinear dynamical systems. The basic idea to avoid this sensitivity is to run the model many times under several slightly-different initial…
The efficiency of statistical sampling in broad-histogram Monte Carlo simulations can be considerably improved by optimizing the simulated extended ensemble for fastest equilibration. Here we describe how a recently developed feedback…
An empirical study was carried out to compare different implementations of ensemble models aimed at improving prediction in spectroscopic data. A wide range of candidate models were fitted to benchmark datasets from regression and…
The equivalence of thermodynamic ensembles is at the heart of statistical mechanics and central to our understanding of equilibrium states of matter. Recently, it has been shown that there is a formal connection between the dynamics of open…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
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…
We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the…
The mean-field thermodynamic limit is studied for a class of isolated Newtonian N-body systems whose Hamiltonian admits several invariants of motion. It is shown that the macrostates of individual members of a statistical equilibrium…
General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible…
We show that entropy is globally concave with respect to energy for a rich class of mean field interactions, including regularizations of the the point-vortex model in the plane, plasmas and self-gravitating matter in 2D, as well as the…