Statistical mechanics of one-dimensional solitary-wave-bearing scalar fields: Exact results and ideal-gas phenomenology

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.

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Statistical mechanics of one-dimensional Ginzburg-Landau fields: Feynman graph evaluation of the screening approximation (n-1expansion)

Journal of Physics A Mathematical Nuclear and General ◽

10.1088/0305-4470/7/17/009 ◽

1974 ◽

Vol 7 (17) ◽

pp. 2144-2151 ◽

Cited By ~ 24

Author(s):

A J Bray

Keyword(s):

Statistical Mechanics ◽

Feynman Graph ◽

Ginzburg Landau ◽

One Dimensional

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The combined effect of lattice’s uniaxial strains and electron–phonon interaction’s screening on TBEC of the intersite bipolarons

International Journal of Modern Physics B ◽

10.1142/s0217979216501861 ◽

2016 ◽

Vol 30 (26) ◽

pp. 1650186

Author(s):

B. Yavidov ◽

SH. Djumanov ◽

T. Saparbaev ◽

O. Ganiyev ◽

S. Zholdassova ◽

...

Keyword(s):

Ideal Gas ◽

Einstein Condensation ◽

Chain Model ◽

One Dimensional ◽

Electron Phonon Interaction ◽

Model Lattice ◽

Experimental Values ◽

Bose Einstein ◽

Derivatives Of ◽

The Ideal

Having accepted a more generalized form for density-displacement type electron–phonon interaction (EPI) force we studied the simultaneous effect of uniaxial strains and EPI’s screening on the temperature of Bose–Einstein condensation [Formula: see text] of the ideal gas of intersite bipolarons. [Formula: see text] of the ideal gas of intersite bipolarons is calculated as a function of both strain and screening radius for a one-dimensional chain model of cuprates within the framework of Extended Holstein–Hubbard model. It is shown that the chain model lattice comprises the essential features of cuprates regarding of strain and screening effects on transition temperature [Formula: see text] of superconductivity. The obtained values of strain derivatives of [Formula: see text] [Formula: see text] are in qualitative agreement with the experimental values of [Formula: see text] [Formula: see text] of La[Formula: see text]Sr[Formula: see text]CuO4 under moderate screening regimes.

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