Related papers: Reinterpreting Boltzmann's H-theorem in the light …
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
This paper proposes to build a bridge between microscopic descriptions of matter with internal energy, composed of many fast interacting particles inside an environment, and their port-Hamiltonian (PH) descriptions at macroscopic scale. The…
We start with reviewing the origin of the idea that entropy and the Second Law are associated with the Arrow of Time. We then introduced a new definition of entropy based on Shannons Measure of Information, SMI. The SMI may be defined on…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
Boltzmann defined the entropy of a macroscopic system in a macrostate $M$ as the $\log$ of the volume of phase space (number of microstates) corresponding to $M$. This agrees with the thermodynamic entropy of Clausius when $M$ specifies the…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
Whereas the original Boltzmann's $H$-theorem applies to elastic collisions, its rigorous generalization to the inelastic case is still lacking. Nonetheless, it has been conjectured in the literature that the relative entropy of the velocity…
Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up…
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…
A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…
What is the best description that we can construct of a thermodynamic system that is not in equilibrium, given only one, or a few, extra parameters over and above those needed for a description of the same system at equilibrium? Here, we…
We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…
A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new…
The combinatorial basis of entropy by Boltzmann can be written $H= {N}^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy of a system, per unit entity, $N$ is the number of entities and $\mathbb{W}$ is the number of ways in which…
Regardless of studies and debates over a century, the statistical origin of the second law of thermodynamics still remains illusive. One essential obstacle is the lack of a proper theoretical formalism for non-equilibrium entropy. Here I…
We propose a new thermodynamic, relativistic relationship between information and entropy, which is closely analogous to the classic Maxwell electro-magnetic equations. Determination of whether information resides in points of…
Before the thermodynamic limit, macroscopic averages need not commute for a quantum system. As a consequence, aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis, when dealing with several…
A mathematical framework for information-theoretic analysis is established, with a new viewpoint of describing transmitted messages and communication channels by the nonlinear expectation theory, beyond the framework of classical…