Related papers: Approaching a large deviation theory for complex s…
The Boltzmann-Gibbs probability distribution, seen as a statistical model, belongs to the exponential family. Recently, the latter concept has been generalized. The q-exponential family has been shown to be relevant for the statistical…
Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like…
We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…
A proof of the relativistic $H$-theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics…
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization.…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
We investigate the non-equilibrium large deviations function of the particle densities in two steady-state driven systems exchanging particles at a vanishing rate. We first derive through a systematic multi-scale analysis the coarse-grained…
The theory of probability shows that, as the fraction $X_n/Y\to 0$, the conditional probability for $X_n$, given $X_n+Y \in h_{\delta}:=[h, h+\delta]$, has a limit law $f_{X_n}(x)e^{-\psi_n(h_\delta)x}$, where $\psi_n(h_\delta) $ equals to…
We develop a relativistic lattice Boltzmann (LB) model, providing a more accurate description of dissipative phenomena in relativistic hydrodynamics than previously available with existing LB schemes. The procedure applies to the…
The aim of this study is tree-fold. First, we investigate the thermodynamics of the Ising models with respect to 2-multiple Hamiltonians. This extends the previous results of [Chazotte and Redig, Electron. J. Probably., 2014] to…
Macroscopic fluctuation theory has shown that a wide class of non-equilibrium stochastic dynamical systems obey a large deviation principle, but except for a few one-dimensional examples these large deviation principles are in general not…
We consider the random point processes on a measure space X defined by the Gibbs measures associated to a given sequence of N-particle Hamiltonians H^{(N)}. Inspired by the method of Messer-Spohn for proving concentration properties for the…
We show that within classical statistical mechanics without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical…
The quantum dynamics away from equilibrium is of fundamental interest for interacting many-body systems. In this letter, we study tilted many-body systems using the effective Hamiltonian derived from the microscopic description. We first…
The classic central limit theorem and $\alpha$-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the…
We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs $\Gamma$-space. Using paradigmatic first-neighbor models,…
Transition state theory (TST) is generalized for the nonequilibrium system with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by the…
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.…