Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 187

Thisresult can be immediatelyobtained if weconsider the process as a

“chemical” reaction

or

For chemicalequilibrium

Since, for photons, we have

where is thechemicalpotential of anideal gas (seepart(e)).Thisresult
gives us (S.4.74.13).

e) Pair creation andannihilation can bewritten in the form

The chemicalpotential of the photon gas is zero(since thenumber ofpho-

tons is not constant but is defined by equilibrium conditions). Therefore,

we have forprocess(S.4.74.14) inequilibrium:

where and are the chemicalpotentials of electrons and positrons,

respectively. If we disregard the walls ofthe box and assume thatthere are

no electrons inside the box initially,then the number of electronsequals

the number of positrons, and Wethen find for the number of

electrons (positrons)

where the factor 2 comesfrom thedouble degeneracy of the electron gas

and we set The energy may be written