Related papers: Reinterpreting Boltzmann's H-theorem in the light …
A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
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…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…
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…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
In 1988, Constantino Tsallis proposed an extension of the Boltzmann statistical mechanics by postulating a new entropy formula, $S_q = k_B\ln_q W$, where $W$ is the number of microstates accessible to the system, and $\ln_q$ defines a…
Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and…
We consider a previously proposed non-extensive statistical mechanics in which the entropy depends only on the probability, this was obtained from a f(\beta) distribution and its corresponding Boltzmann factor. We show that the first term…
Fluctuation theorems impose fundamental bounds in the statistics of the entropy production, with the second law of thermodynamics being the most famous. Using information theory, we quantify the information of entropy production and find an…
The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data…
In this work we develop on the recently suggested concept of superstatistics [C. Beck and E.G.D. Cohen, Physica A {\bf 322}, 267 (2003)], face the problem of devising a viable way for estimating the correct statistics for a system in…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Maxwell's velocity distribution is known to be universally valid across systems and phases. Here we present a new and general derivation that uses the central limit theorem (CLT) of the probability theory. This essentially uses the idea…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
In this article, we review a general theoretical framework of thermodynamics of information on the basis of Bayesian networks. This framework can describe a broad class of nonequilibrium dynamics of multiple interacting systems with complex…
We examine the {combinatorial} or {probabilistic} definition ("Boltzmann's principle") of the entropy or cross-entropy function $H \propto \ln \mathbb{W}$ or $D \propto - \ln \mathbb{P}$, where $\mathbb{W}$ is the statistical weight and…
An essential role of information in microscopic thermodynamics (e.g. Maxwell's demon) opens a challenging question if there exists a formulation of the second law of thermodynamics based only on pure information ideas. Here, such a…
We propose a new perspective on Turbulence using Information Theory. We compute the entropy rate of a turbulent velocity signal and we particularly focus on its dependence on the scale. We first report how the entropy rate is able to…