Related papers: Nonextensive statistical mechanics and economics
We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasi-stationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution,…
Starting from metric of the general nonextreme stationary axisymmetric black hole in four-dimensional spacetime, both statistical-mechanical and thermodynamical entropies are studied. First, by means of the "brick wall" model in which the…
Stochastic Thermodynamics (ST) extends the notions of classical thermodynamics to trajectories taken from a nonequilibrium ensemble. This extension yields a simple approach to fluctuation relations in small systems. Multiple time- and…
We consider an overdamped Brownian particle subject to an asymptotically flat potential with a trap of depth $U_0$ around the origin. When the temperature is small compared to the trap depth ($\xi=k_B T/U_0 \ll 1$), there exists a range of…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
Within the description of stochastic differential equations it is argued that the existence of Boltzmann-Gibbs type distribution in economy is independent of the time reversal symmetry in econodynamics. Both power law and exponential…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
Conventional Boltzmann--Gibbs statistical mechanics successfully describes systems with weak to moderate correlations, where the number of accessible configurations $W(N)$ grows exponentially with the number of degrees of freedom~$N$.…
A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy $S_{BG}$ and its associated exponential BG factor. Frequent…
As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium…
The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta. This leads to modifications of some of thermodynamic…
A heuristic generalization of the Boltzmann-Gibbs microcanonical entropy is proposed, able to describe meta-equilibrium features and evolution of macroscopic systems. Despite its simple-minded derivation, such a function of "collective…
The incomplete nonextensive statistics in the canonical and microcanonical ensembles is explored in the general case and in a particular case for the ideal gas. By exact analytical results for the ideal gas it is shown that taking the…
The statistical mechanics of a cloud of particles interacting via their gravitational potentials is an old problem which encounters some issues when the traditional Boltzmann-Gibbs statistics is applied. In this article, we consider the…
The statistical methods based on the classical Boltzmann-Gibbs (BG) approach are at heart of essentially all descriptions of multiparticle production processes. In many cases, however, one observes some deviations from the expected…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…
After a brief review of the present status of nonextensive statistical mechanics, we present a conjectural scenario where mixing (characterized by the entropic index $q_{mix} \le 1$) and equilibration (characterized by the entropic index…
The use of statistical methods to model gravitational systems is crucial to physics practice, but the extent to which thermodynamics and statistical mechanics genuinely apply to these systems is a contentious issue. This paper provides new…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…