15 Statistics under extreme conditions
In most ofthisbook,wehavebeendealingwithconventionalmaterials. However,
statistical physics can be useful in a number of situations where the environment is
anything other than ordinary.
One ofthese situations concerns superfluidity. Superfluidstates are normallyasso-
ciated with extremes of low temperature, although nowadays the advent of ‘high’
temperature superconductivitybrings them nearer to ourdirect experience. Wehave
alreadycoveredquite alot about BE superfluidsandsuperfluidityinliquid^4 He in
earlier chapters (9 and 14). But more surprising, and more exotic, is the existence
of superfluid states in FD systems, and this is the topic of section 15.1. At the other
end of the spectrum, there are surprisinglyimportant roles for statistical physics in
our understanding of the stability of white dwarf and neutron stars, and these are
discussed in section 15.2, together with a few comments about cosmologyand the
bigbang.
15 .1 Superfluid states in Fermi–Dirac systems
In our treatment ofgases, wehave seen that anidealBEgas (Chapter 9) atlow
temperatures becomes ordered byhavingall of its particles enter the sameground
state. The assembly ground state (atT=0) is simply the symmetric combination
whichhas allNindividualparticlesinthe same,lowest one-particle state. As wehave
seen, this type of coherent occupation of a single quantum state byall the particles
gives a valuable (if imperfect, Chapter 14) picture of the superfluidity observed in
liquid^4 Hebelow2.17 K.
An FD gas becomes ordered in a very different way, with the assembly ground
statebeingdominatedbythe Pauliexclusion principle. Since allone-particle states
can nowbe at most singlyoccupied,the assembly groundstate (Chapter 8)hasfull
occupation for the one-particle states with energies up to the Fermi energyμ( 0 ),and
zero occupationfor those withhigher energies. This providesawell-ordered(zero
entropy) state, asis appropriate toT= 0 ,but the stateis one ofconsiderable energy,
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