Statistical mechanics of an ideal gas

2009 ◽  
pp. 233-243
Author(s):  
Stephen J. Blundell ◽  
Katherine M. Blundell
Keyword(s):  
Statistical Mechanics ◽  
Ideal Gas

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.

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

1980 ◽  
Vol 22 (2) ◽  
pp. 477-496 ◽  
Author(s):  
J. F. Currie ◽  
J. A. Krumhansl ◽  
A. R. Bishop ◽  
S. E. Trullinger
Keyword(s):  
Solitary Wave ◽  
Statistical Mechanics ◽  
Scalar Fields ◽  
Ideal Gas ◽  
Exact Results ◽  
One Dimensional

Yang–Yang equilibrium statistical mechanics: A brilliant method

2016 ◽  
Vol 30 (09) ◽  
pp. 1630008
Author(s):  
Xi-Wen Guan ◽  
Yang-Yang Chen
Keyword(s):  
Statistical Mechanics ◽  
Weak Interactions ◽  
Delta Function ◽  
Ideal Gas ◽  
Baxter Equation ◽  
Dimensional System ◽  
Equilibrium Statistical Mechanics ◽  
Rigorous Approach ◽  
Wide Range ◽  
The One

Yang and Yang in 1969 [J. Math. Phys. 10, 1115 (1969)] for the first time proposed a rigorous approach to the thermodynamics of the one-dimensional system of bosons with a delta-function interaction. This paper was a breakthrough in exact statistical mechanics, after Yang [Phys. Rev. Lett. 19, 1312 (1967)] published his seminal work on the discovery of the Yang–Baxter equation in 1967. Yang and Yang’s brilliant method yields significant applications in a wide range of fields of physics. In this paper, we briefly introduce the method of the Yang–Yang equilibrium statistical mechanics and demonstrate a fundamental application of the Yang–Yang method for the study of thermodynamics of the Lieb–Liniger model with strong and weak interactions in a whole temperature regime. We also consider the equivalence between the Yang–Yang’s thermodynamic Bethe ansatz equation and the thermodynamics of the ideal gas with the Haldane’s generalized exclusion statistics.

scholarly journals BEC IN NONEXTENSIVE STATISTICAL MECHANICS

2000 ◽  
Vol 14 (04) ◽  
pp. 405-409 ◽  
Author(s):  
LUCA SALASNICH
Keyword(s):  
Transition Temperature ◽  
Statistical Mechanics ◽  
Dimensional Space ◽  
Ideal Gas ◽  
Einstein Condensation ◽  
Nonextensive Statistical Mechanics ◽  
Small Deviations ◽  
Bose Einstein Condensation ◽  
Bose Statistics ◽  
Bose Einstein

We discuss the Bose–Einstein condensation (BEC) for an ideal gas of bosons in the framework of Tsallis's nonextensive statistical mechanics. We study the corrections to the st and ard BEC formulas due to a weak nonextensivity of the system. In particular, we consider three cases in the D-dimensional space: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. The results show that small deviations from the extensive Bose statistics produce remarkably large changes in the BEC transition temperature.

scholarly journals Statistical mechanics of an ideal gas of non-Abelian anyons

2013 ◽  
Vol 867 (3) ◽  
pp. 950-976 ◽  
Author(s):  
Francesco Mancarella ◽  
Andrea Trombettoni ◽  
Giuseppe Mussardo
Keyword(s):  
Statistical Mechanics ◽  
Ideal Gas

scholarly journals BEC IN NONEXTENSIVE STATISTICAL MECHANICS: SOME ADDITIONAL RESULTS

2001 ◽  
Vol 15 (09) ◽  
pp. 1253-1256 ◽  
Author(s):  
LUCA SALASNICH
Keyword(s):  
Transition Temperature ◽  
Statistical Mechanics ◽  
Previous Analysis ◽  
Ideal Gas ◽  
Einstein Condensation ◽  
Nonextensive Statistical Mechanics ◽  
Bose Einstein Condensation ◽  
Analytical Formulas ◽  
Bose Einstein ◽  
Ideal Bose Gas

In a recent paper1 we discussed the Bose–Einstein condensation (BEC) in the framework of Tsallis's nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction.

scholarly journals Statistical Mechanics of Unconfined Systems: Challenges and Lessons

2021 ◽  
Vol 3 (1) ◽  
pp. 8
Author(s):  
Bruno Arderucio Costa ◽  
Pedro Pessoa
Keyword(s):  
Probability Distribution ◽  
Statistical Mechanics ◽  
Maximum Entropy ◽  
A Priori ◽  
Ideal Gas ◽  
Stationary Probability ◽  
De Sitter ◽  
Stationary Probability Distribution ◽  
Local Measurements ◽  
Priori Information

Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space of an unconfined ideal gas in an anti-de Sitter background. Notwithstanding the gas’ freedom to move in an infinite volume, we establish necessary conditions for the stationary probability distribution solving a general maximum entropy problem to be normalizable and obtain the resulting probability for a particular choice of constraints. As a part of our analysis, we develop a novel method for identifying dynamical constraints based on local measurements. With no appeal to a priori information about globally defined conserved quantities, it is therefore applicable to a much wider range of problems.

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