scholarly journals Probability, Entropy, and Gibbs’ Paradox(es)

Entropy ◽  
2018 ◽  
Vol 20 (6) ◽  
pp. 450 ◽  
Author(s):  
Robert Swendsen
Keyword(s):  
Gibbs Paradox

scholarly journals Mixing indistinguishable systems leads to a quantum Gibbs paradox

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Benjamin Yadin ◽  
Benjamin Morris ◽  
Gerardo Adesso
Keyword(s):  
Statistical Mechanics ◽  
Thought Experiment ◽  
Entropy Change ◽  
Ideal Gas ◽  
Gibbs Paradox ◽  
Quantum Case ◽  
Entropy Increase ◽  
Level Of Knowledge ◽  
Different Gases ◽  
As If

AbstractThe 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, who cannot distinguish the gases, has no way of extracting work by mixing them. Moving the thought experiment into the quantum realm, we reveal new and surprising behaviour: the ignorant observer can extract work from mixing different gases, even if the gases cannot be directly distinguished. Moreover, in the macroscopic limit, the quantum case diverges from the classical ideal gas: as much work can be extracted as if the gases were fully distinguishable. We show that the ignorant observer assigns more microstates to the system than found by naive counting in semiclassical statistical mechanics. This demonstrates the importance of accounting for the level of knowledge of an observer, and its implications for genuinely quantum modifications to thermodynamics.

Mathematical solution of the Gibbs paradox

2011 ◽  
Vol 89 (1-2) ◽  
pp. 266-276 ◽  
Author(s):  
V. P. Maslov
Keyword(s):  
Gibbs Paradox ◽  
Mathematical Solution

Extensivity of entropy and modern form of Gibbs paradox

Pramana ◽  
1981 ◽  
Vol 17 (6) ◽  
pp. 509-514 ◽  
Author(s):  
D Home ◽  
S Sengupta
Keyword(s):  
Gibbs Paradox ◽  
Modern Form

On the Occurrence of Gibbs Paradox

2019 ◽  
Vol 48 (3) ◽  
pp. 77-88
Author(s):  
Davide Giusti ◽  
Vincenzo G. Molinari
Keyword(s):  
Gibbs Paradox

scholarly journals The Gibbs Paradox

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 552 ◽  
Author(s):  
Simon Saunders
Keyword(s):  
Statistical Mechanics ◽  
Cartesian Product ◽  
Classical Case ◽  
Particle State ◽  
Gibbs Paradox ◽  
Quantum Case ◽  
State Spaces ◽  
Open Questions ◽  
Thermodynamics And Statistical Mechanics ◽  
Sequence Position

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 quantum theory (there is no classical solution), some to classical theory (the quantum case is different). The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability (in the classical case, Gibbs’ notion of ‘generic phase’). Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level of the tensor (or Cartesian) product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. ‘Distinguishability’, in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction.

The Gibbs Paradox

1984 ◽  
pp. 303-312 ◽  
Author(s):  
N.G. van Kampen
Keyword(s):  
Gibbs Paradox
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