Related papers: The Gibbs Paradox
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…
The Gibbs paradox has frequently been interpreted as a sign that particles of the same kind are fundamentally indistinguishable; and that quantum mechanics, with its identical fermions and bosons, is indispensable for making sense of this.…
The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical…
Identical classical particles are distinguishable. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and from the relation S = k ln W leads to a non-extensive expression for the entropy.…
We show in this note that Gibbs paradox arises not due to application of thermodynamic principles, whether classical or statistical or even quantum mechanical, but due to incorrect application of mathematics to the process of mixing of…
The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small…
The classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is that an "ignorant" observer,…
The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs' paradox. Granted that it is as much at home in classical as in quantum statistical…
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…
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…
We present a fully quantum solution to the Gibbs paradox (GP) with an illustration based on a gedanken experiment with two particles trapped in an infinite potential well. The well is divided into two cells by a solid wall, which could be…
The article reveals the error that in classical thermodynamics leads to the Gibbs paradox. The essence of the error lies in the fact that the entropy of an ideal gas is attributed to additive quantities, but it is not correct. The value of…
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…
The Gibbs Mixing Paradox is a conceptual touchstone for understanding mixtures in statistical mechanics. While debates over the theoretical subtleties of particle distinguishability continue to this day, we seek to extend the discussion in…
The analysis of the arguments within the limits of the classical thermodynamics that lead to the Gibbs paradox was made. Features of preconditions used in the derivation of the entropy of mixing of ideal gases that caused the appearance of…
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the…
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…
It is shown that the Gibbs paradox is actually paralogism, viz. an erroneous statement sounding credible due to the statistic-mechanical interpretation of entropy as a measure of "any and all" irreversibility. As an alternative, the…
As no heat effect and mechanical work are observed, we have a simple experimental resolution of the Gibbs paradox: both the thermodynamic entropy of mixing and the Gibbs free energy change are zero during the formation of any ideal…
We consider the Statistical Mechanics of systems of particles satisfying the $q$-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (resp.\ Fermi) relations for…