Fluctuations en pression

Münster, Arnold

doi:10.1016/0031-8914(60)90144-0

Cited by 10 publications

(12 citation statements)

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“…According to the famous Gibbs lemma [1] (Ch. VII, equations (252), (255), see also [3] and [5]), the equilibrium pressure fluctuations (∆P (Γ)) 2 are given by the expression…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Finally, averaging the Ψ V (Γ) according to (1) gives Ψ(β, V ) and thus allows us to obtain in quite general way the solution of the long-standing and rather controversial problem [2][3][4][5][6][7][8] of thermal equilibrium pressure fluctuations (3) in isothermal-isochoric Gibbs ensemble for the nonideal systems of particles in classical regime.…”

Section: Solution Of the Problemmentioning

confidence: 99%

“…In 1902 Gibbs [1], Ch.VII, proved his famous Lemma and wrote down the appropriate expression, which includes the quantity named by him the "dynamical compressibility"; see also Fowler [2], Hill [3], Kittel [4], Terletzky [5] (more precise definitions are given below).…”

Section: Introductionmentioning

confidence: 99%

“…Some "pessimistic" point of view was expressed in [3], Ch. 4, §19 (see also [5], §69), where the calculation of the pressure fluctuations was connected with the detailed knowledge of the kind of forces acting between the gas particles and the container walls. Unfortunately, some attempts [2,3] to follow this route brought to physically unsatisfactory -i. e., divergent -results.…”

Section: Introductionmentioning

confidence: 99%

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The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics

Rudoy¹

2009

Condens. Matter Phys.

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The long-standing and highly non-trivial problem of calculating the pressure fluctuations in the Gibbs equilibrium statistical mechanics is fully revised. The previous attempts are critically analyzed and it is shown that the application of the ideas by Bogolyubov gives the full and unambiguous solution of this problem. The crucial role is played by the Bogolyubov's idea of quasiaverages (or rather quasidynamic) quantities -specifically, the pressure P and dynamic compressibility Ψ. The virtual conjugate field which eliminates the translational invariance of the Hamilton function H in the limit ε →0 is the singular potential of the impenetrable walls of the container. The general relations for P and Ψ in terms of the derivatives of H are obtained and some examples are studied -i. e., the cases of the ideal vs. non-ideal as well as of uniform vs. non-and quasi-uniform (in Euler sense) Hamilton function H describing the given system.

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“…According to the famous Gibbs lemma [1] (Ch. VII, equations (252), (255), see also [3] and [5]), the equilibrium pressure fluctuations (∆P (Γ)) 2 are given by the expression…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Solution Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics

Rudoy¹

2009

Condens. Matter Phys.

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“…Many unsuccessful attempts were undertaken for calculating this quantity even for the simplest case of 'ordinary' non-relativistic ideal gas. One can find the details in the works by Fowler [2], Wergeland [6], Münster [7], and M. Klein [8].…”

Section: Introductionmentioning

confidence: 99%

Generalizing Bogoliubov–Zubarev Theorem to Account for Pressure Fluctuations: Application to Relativistic Gas

Rudoy

Rybakov

2019

Particles

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The problem of pressure fluctuations in the thermal equilibrium state of some objects is discussed, its solution being suggested via generalizing the Bogoliubov–Zubarev theorem. This theorem relates the thermodynamic pressure with the Hamilton function and its derivatives describing the object in question. It is shown that unlike to other thermodynamic quantities (e.g., the energy or the volume) the pressure fluctuations are described not only by a purely thermodynamic quantity (namely, the corresponding thermodynamic susceptibility) but also by some non-thermodynamic quantities. The attempt is made to apply these results to the relativistic ideal gases, with some numerical results being valid for the limiting ultra-relativistic or high-temperature case.

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Statistical mechanics of adiabatic processes

Mountain¹

1964

Physica

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Fluctuations en pression

Cited by 10 publications

References 1 publication

The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics

The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics

Generalizing Bogoliubov–Zubarev Theorem to Account for Pressure Fluctuations: Application to Relativistic Gas

Statistical mechanics of adiabatic processes

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