Gas

In General > s.a. Kinetic Theory; matter.
* Idea: A highly compressible fluid, in which the mean interparticle distance is much greater than their size.
@ References: Rohrmann PhyA(05)cm/04 [statistical mechanics, new formalism]; Seiringer a0908 [cold gases, mathematical].
> Related topics: see fluctuations; statistical mechanics.

Ideal Gas > s.a. fluids; specific heat; thermodynamical systems [including geometry of state space].
* Idea: A large collection of particles with no internal structure, non-interacting except for collisions (small hard spheres).
* Equation of state: The ideal gas law

pV = nRT = Nk_BT ,

where R is the molar gas constant, and k_B the Boltzmann constant (> see constants).
* Remark: Most gases at room T and p behave like ideal gases, but as T → 0 they can't because of quantum effects.
* Internal energy: If s is the number of degrees of freedom (s = 3 for a monatomic gas),

U = (s/2) Nk_BT .

* Entropy: Given by

S = C_V ln(T/T₀) + Nk_B ln(V/V₀) .

* Consequences: Aerosol cans get cold when used.
* In gravitational field: The equilibrium pressure of a perfect gas in a constant gravitational field decreases exponentially with height (barometric formula).
@ Quantum: Meyer qp/97 [quantum lattice gas]; Bloch pw(04)apr [in optical lattices]; Nattermann AJP(05)apr [scaling approach]; Velenich et al JPA(08) [Brownian gas, Poissonian ground state]; Dodonov & Vieira Lopes PLA(08) [temperature increase from sudden expansion]; > s.a. quantum-gravity phenomenology.
@ Relativistic: Becattini & Piccinini AP(08), Becattini & Tinti a0911 [rotating].
@ Related topics: Landsberg et al AJP(94)aug, Pantellini AJP(00)jan [in constant g field]; Creaco & Kalogeropoulos MPLB(09)-a0811 [thermodynamic limit, phase space measure]; > s.a. Boltzmann Equation; Maxwell-Boltzmann Distribution.

Self-Gravitating Gas
@ Statistical mechanics: de Vega et al CSF(99)ap/98; de Vega & Sánchez PLB(00), NPB(02)ap/01, NPB(02)ap/01; de Vega & Siebert PRE(02)ap/01; de Vega & Sánchez ap/05-in, CRS(06)ap.
@ Related topics: de Vega & Sánchez NPB(05)ap/03 [cluster expansion]; de Vega & Siebert NPB(05) [with dark energy]; Siebert PhD(05)ap; > s.a. gravitating matter.

Other Types > s.a. Chaplygin Gas; composite quantum systems; diffusion; loops; Virial Expansion; Viscosity.
* Granular gases: The main characteristic of a granular gas, which makes it fundamentally different from ordinary molecular gases, is its tendency to form clusters, i.e. to spontaneously separate into dense and dilute regions.
@ Photons: Leff AJP(02)aug [in introductory physics]; > s.a. Adiabatic Transformation; modified lorentz group.
@ Bosons: Lenard JMP(66) [1D, impenetrable]; Chuu et al PRL(05) [sub-Poissonian number fluctuation]; Toms JPA(06) [statistical mechanics, confined geometry]; Deuar & Drummond JPA(06) [interacting]; Martin IJTP(05) [repulsive potential, polymer representation]; Nattermann AJP(07)oct [weakly interacting, from heuristics and thermodynamics]; Erdos et al a0806 [ground-state energy]; Giuliani & Seiringer JSP(09) [high density, ground-state energy]; Babichenko & Babichenko PLA(09) [in random external field]; > s.a. Bose-Einstein Condensation.
@ Fermions: Elze et al JPG(80) [ideal, relativistic]; Jin pw(02)apr [of atoms]; Thomas & Gehm AS(04)#3 [cold, optically trapped]; Seiringer CMP(06)mp/04 [pressure]; Lieb et al mp/05-in [dilute, ground-state energy]; Chang & Pandharipande PRL(05) [strongly interacting, ground state]; Leboeuf & Roccia PRL(06) [2-component, level density]; Kowalski et al PRD(07)-a0712 [relativistic, T = 0]; Jaksic et al CMP(09) [locally interacting, central limit theorem]; Giorgini et al RMP(08) [ultracold]; Jo et al Sci(09)sep [ferromegnatism]; > s.a. Hartree-Fock Equation.
@ Non-ideal gases: Coutant & Rajeev a0807 [quantum thermodynamics]; > s.a. extended thermodynamics [dense gases].
@ Granular gases: Brilliantov & Pöschel 04 [r JPA(05)#47]; Van der Weele CP(08) [clustering].
@ Other types: Dimock JSP(09)-a0812 [dipole gas, infinite-volume limit].

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