Related papers: Information Theory and Statistical Mechanics Revis…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to…
Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization $\sum_{i=1}^wp_i^q=1$ is used to obtain generalized entropy $S=-k\sum_{i=1}^wp_i^q\ln…
The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of…
In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…
Recent progress has shown that the generalization error of the Gibbs algorithm can be exactly characterized using the symmetrized KL information between the learned hypothesis and the entire training dataset. However, evaluating such a…
Information (I) is defined as the amount of the data after data compression. The first law of information theory: the total amount of data L (the sum of entropy S and information I) of an isolated system remains unchanged. The second law of…
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 can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to…
The paper moves a step towards the full integration of statistical mechanics and information theory. Starting from the assumption that the thermodynamical system is composed by particles whose quantized energies can be modelled as…
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…
In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Gibbs law characterized by an effective temperature equal to the average amount of…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
In this paper we investigate the applicability of non-equilibrium statistical mechanics to non-equilibrium damage phenomena. As an example, a fiber-bundle model with thermal noise and a fiber-bundle model with decay of fibers are…
For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically…
We present a novel derivation of the constraints required to obtain the underlying principles of statistical mechanics using a maximum entropy framework. We derive the mean value constraints by use of the central limit theorem and the…