Related papers: Infinite ergodic theory meets Boltzmann statistics
When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more…
It is shown that time reversibility of Hamiltonian microscopic dynamics and Gibbs canonical statistical ensemble of initial conditions for it together produce an exact virial expansion for probability distribution of path of molecular…
On a fine grained scale the Gibbs entropy of an isolated system remains constant throughout its dynamical evolution. This is a consequence of Liouville's theorem for Hamiltonian systems and appears to contradict the second law of…
A statistical treatment of finite unbound systems in the presence of collective motions is presented and applied to a classical Lennard-Jones Hamiltonian, numerically simulated through molecular dynamics. In the ideal gas limit, the flow…
In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage…
We reconsider the Boltzmann-Gibbs statistical ensemble in thermodynamics using the multinomial coefficient approach. We show that an ensemble is defined by the determination of four statistical quantities, the element probabilities $p_i$,…
Brownian yet non-Gaussian diffusion has recently been observed in numerous biological and active matter system. The cause of the non-Gaussian distribution have been elaborately studied in the idea of a superstatistical dynamics or a…
We derive an equation for the current of particles in energy space; particles are subject to a mean field effective potential that may represent quantum effects. From the assumption that non-interacting particles imply a free diffusion…
We consider Canonical Gibbsian ensembles of Euler point vortices on the 2-dimensional torus or in a bounded domain of R 2 . We prove that under the Central Limit scaling of vortices intensities, and provided that the system has zero global…
We study mathematically the equilibrium properties of the Bose-Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the energy and the number of particles. We establish the equivalence between the…
Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular…
We study ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin/fat tailed distributions, the normalized/non-normalised invariant…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of…
It is shown that in adiabatic approximation for nuclei the many-component Coulomb system cannot be described on the basis of the grand canonical ensemble. Using the variational Bogolyubov's procedure for the free energy, the Hohenberg-Kohn…
We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation.…