1 2 Two new ideas
Inthischapter we shallexplorebriefly two concepts whichindicate that statistical
physicsis not sucha restrictive subject as mightatfirst appear. The secondgives clear
pointers as to how we can start to deal with interacting particles. But before that, we
shallconsider connectionsbetween thermalequilibrium properties andtransitions
between states.
1 2.1 Statics or dynamics?
Thermalequilibrium really isallabout transitions,inspite ofits static (andboring?)
sound.As stressed in Chapter 1, our assembly samples effectively all its possible states
over thetime ofan experiment, otherwise thewhole concept ofthermalequilibrium
becomes misty.Theidea ofadynamic equilibriumgives allsorts ofconnections
between equilibrium and transport properties. In this section we explore just one
suchconnection.
1 2.1.1 Matter and radiation in equilibrium
This is hardly a new topic, since it was introduced by Einstein. However, it is partic-
ularlyimportantbecauseitbrings together the properties ofmatter andradiationin
thermalequilibrium, alongwithan understandingoftheemission andabsorption of
radiation by matter.
Consider abox whichcontainsbothradiation anda number ofatoms, all inthermal
equilibrium at temperatureT.To be specific suppose the atoms are localizedparticles,
which have two energy states, separated by(they may have other energy states also,
but these areirrelevant). Let therebeNNN 2 atomsintheupper state, andN 1 inthelower
state. One thingwe have proved (Chapter 2) is that in equilibrium the ratio of the
numbers of atoms in the two states is given by the Boltzmann factor
NNN 2 /N 1 =exp(−/kkkBT) (2.26)and(12.1)What about theradiation? Thermalequilibriumisdescribedin section 9.3. Thepho-
tons occupystates ofenergyεwithan occupationfunction whichisthemodified
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