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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…

Statistical Mechanics · Physics 2007-11-09 Stephen R. Williams , Denis J. Evans

Modern biomedical, behavioral and psychological inference about cause-effect relationships respects an ergodic assumption, that is, that mean response of representative samples allow predictions about individual members of those samples.…

Neurons and Cognition · Quantitative Biology 2021-05-31 Madhur Mangalam , Damian G. Kelty-Stephen

We brief{}ly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermodynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs~(BG) statistical…

Statistical Mechanics · Physics 2014-11-03 Constantino Tsallis , Leonardo J. L. Cirto

Gibbsian statistical mechanics (GSM) is the most widely used version of statistical mechanics among working physicists. Yet a closer look at GSM reveals that it is unclear what the theory actually says and how it bears on experimental…

Statistical Mechanics · Physics 2018-07-12 Roman Frigg , Charlotte Werndl

Boltzmann-Gibbs statistical mechanics is based on the entropy $S_{BG}=-k \sum_{i=1}^W p_i \ln p_i$. It enables a successful thermal approach of ubiquitous systems, such as those involving short-range interactions, markovian processes, and,…

Statistical Mechanics · Physics 2009-11-10 Constantino Tsallis , Edgardo Brigatti

The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic non-stationary statistical properties of its fluctuations. Here, we study…

Statistical Mechanics · Physics 2011-12-13 Adrian A. Budini

We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how…

Statistical Mechanics · Physics 2015-03-02 J. P. Badiali

A variety of phenomena in nuclear and high energy physics seemingly do not satisfy the basic hypothesis for possible stationary states to be of the type covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the system…

Statistical Mechanics · Physics 2017-08-23 C. Tsallis , Ernesto P. Borges

Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…

Quantum Physics · Physics 2022-10-31 Brian Drummond

We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…

Dynamical Systems · Mathematics 2011-04-15 Stefano Galatolo , Mathieu Hoyrup , Cristóbal Rojas

We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…

Quantum Physics · Physics 2018-11-20 Chol Jong , Byong-Il Ri , Song-Guk Kim , Son-Il Jo , Shin-Hyok Jon , Namchol Choe

A variety of astronomical phenomena appear to not satisfy the ergodic hypothesis in the relevant stationary state, if any. As such, there is no reason for expecting the applicability of Boltzmann-Gibbs (BG) statistical mechanics. Some of…

Statistical Mechanics · Physics 2011-07-19 Constantino Tsallis , Domingo Prato , Angel R. Plastino

A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…

Mathematical Physics · Physics 2008-11-06 E. D. Belokolos

Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…

Statistical Mechanics · Physics 2025-10-31 O. B. Ericok , J. K. Mason

We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum…

Statistical Mechanics · Physics 2009-11-13 Adi Rebenshtok , Eli Barkai

Many physicists think that the maximum entropy formalism is a straightforward application of Bayesian statistical ideas to statistical mechanics. Some even say that statistical mechanics is just the general Bayesian logic of inductive…

Statistical Mechanics · Physics 2007-05-23 Cosma Rohilla Shalizi

We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for…

Chaotic Dynamics · Physics 2022-05-19 Jiaozi Wang , Giuliano Benenti , Giulio Casati , Wen-ge Wang

We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Merced Montesinos , Carlo Rovelli

We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems [J. M\"uller et al., Phys. Rev. Lett. Phys. Rev. Lett. 133, 217101 (2024)]. The gauge…

Statistical Mechanics · Physics 2025-03-26 Johanna Müller , Florian Sammüller , Matthias Schmidt

We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…

Quantum Physics · Physics 2013-12-13 Agung Budiyono