Related papers: Testing the Foundations of Classical Entropy: Coll…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable…
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…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
Doubts are raised concerning the usual interpretation of the alleged failure, by quantum mechanics, of the distributive law of classical logic. The difficulty raised by incompatible sets of observables is overcome within an epistemic…
In statistical mechanics Gibbs' paradox is avoided if the particles of a gas are assumed to be indistinguishable. The resulting entropy then agrees with the empirically tested thermodynamic entropy up to a term proportional to the logarithm…
Colloidal particles are distinguishable. Moreover, their thermodynamic properties are extensive. Statistical Mechanics predicts such behaviour if one accepts that the configurational integral of a system of N colloids must be divided by N!.…
The Gibbs paradox of the first kind (GP1) refers to the false increase in entropy which, in statistical mechanics, is calculated from the process of combining two gas systems S1 and S2 consisting of distinguishable particles. Presented in a…
A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for…
The mixing of two different gases is one of the most common natural phenomena, with applications ranging from CO$_2$ capture to water purification. Traditionally, mixing is analyzed in the context of local thermal equilibrium, where systems…
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…
This is a systematic review of the concept of indistinguishability in both classical and quantum mechanics, with particular attention to Gibbs' paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of the concept of classical…
We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and prove a series of inequalities relating these measures. We then examine these as a function of the…
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…
Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown…
The formulas for the entropy of ideal gases mixture and the entropy change in mixing of ideal gases on the basis of the third law of thermodynamics were obtained. It is shown that when using these formulas, the Gibbs paradox within the…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
We introduce into classical mechanics the concept of non-discerned particles for particles that are identical, non-interacting and prepared in the same way. The non-discerned particles correspond to an action and a density which satisfy the…
We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while…
This article presents the results of research into the causes of the Gibbs paradox in the formulation discussed by J. W. Gibbs himself. In this formulation, we are talking about an inexplicable (paradoxical) jump in the entropy of mixing of…