Related papers: Information Theory and Statistical Mechanics Revis…
Equilibrium statistical mechanics rests on the assumption of ergodic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a…
We propose a prequential or sequentially predictive formulation of the work extraction where an external agent repeats the extraction of work from a heat engine by cyclic operations based on his predictive strategy. We show that if we…
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…
Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…
Traditionally the exponential canonical distributions of Gibbsian statistical mechanics are given theoretical justification in at least four different ways: steepest descent method, counting method, Khinchin's method based on te central…
The aim of this review is to provide better understanding of a few approaches that have been proposed for treating nonequilibrium (time-dependent) processes in statistical mechanics with the emphasis on the inter-relation between theories.…
We extend the canonical Gibbs distribution, originally formulated for systems at equilibrium, to systems driven out of equilibrium. The stochastic dynamics of a small system are described by a probability distribution over discrete energy…
Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits…
Generalized Probabilistic Theories (GPTs) provide a unified framework for describing probabilistic physical theories, encompassing classical and quantum theories as well as hypothetical theories beyond quantum mechanics. Since most GPTs are…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
In this lecture we briefly review the definition, consequences and applications of an entropy, $S_q$, which generalizes the usual Boltzmann-Gibbs entropy $S_{BG}$ ($S_1=S_{BG}$), basis of the usual statistical mechanics, well known to be…
Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data…
A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory,…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
Biological, artificial, and physical systems dissipate energy to accurately transmit information. While tools of information theory have been used to characterize information-processing capabilities, how reliably this information is…
We study nonequilibrium thermodynamics of complex information flows induced by interactions between multiple fluctuating systems. Characterizing nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain novel…
The local physical properties of an isolated quantum statistical system in the stationary state reached long after a quench are generically described by the Gibbs ensemble, which involves only its Hamiltonian and the temperature as a…
This paper introduces the basic concepts of information theory. Based on these concepts, we regard the states in the state space and the types of ideal gases as the symbols in a symbol set to calculate the mixing entropy of ideal gas…
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…
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…