Statistical Physics, Volume 1

adiabatic process angular momentum assume atoms axis Boltzmann Bose Bravais lattice calculate chemical potential closed system coefficient condition consider const constant corresponding critical point crystal curve degrees of freedom denote density density matrix derivative determined distribution function electron element energy levels entropy equal equation expansion expression external Fermi Fermi gas fluctuations formula free energy gases Gibbs distribution given Hence identical integral interaction kinetic energy kT log liquid macroscopic body matrix mean value molecules motion normalisation number of particles obtain oscillator partition function perfect gas phase space phase transition phonons pressure properties Quantum Mechanics relation result rotation second-order solid solution specific heat spectrum spin substance Substituting subsystem surface symmetry T₁ thermodynamic potential thermodynamic quantities total number transition point V₁ vanish vapour variables vector velocity vibrations volume wave functions zero ӘР