Statistical Physics

atoms axis Bose Bravais lattice calculate chemical potential classical closed system co-ordinates coefficients components concentration condition constant corresponding critical point crystal decreases defined denote density derivative determined distribution function electron elements entropy equal equation expansion expression Fermi gas finite fluctuations formula free energy gases Gibbs distribution given gives Hence ideal gas integral interaction liquid macroscopic body mass matrix mean square mean value molecules momenta motion number of particles obtain P₁ partition function phase space phase transition phonons plane pressure probability problem properties Quantum Mechanics quasi-particles reciprocal lattice regarded relation respect result Rmin rotation second kind solid solution solvent specific heat spectrum spin statistical substance Substituting subsystem suffix surface symmetry temperature thermal thermodynamic potential thermodynamic quantities tion total number transition point V₁ vapour variables vector velocity vibrations volume wave functions zero