Classical statistical mechanics

Some aspects of statistical mechanics that are particularly important for computer simulation approaches are recalled. Using Ising and classical Heisenberg models as examples, various statistical ensembles and appropriate thermodynamic potentials axe introduced, and concepts such as Legendre transformations between ensembles and the thermodynamic integration method to obtain the entropy are mentioned. Probability distributions characterizing statistical fluctuations axe discussed, fluctuation relations for response functions are derived, and the behavior of these quantities at first and second order phase transitions axe described qualitatively. Also the general consequences of phase coexistence will be briefly mentioned, including the extension to surface and interface terms. The last part of this survey then is devoted to nonequilibrium statistical mechanics. The phenomenological description in terms of linear relation between fluxes and thermodynamic driving forces will be mentioned, as well as the linear response approach and Green-Kubo relations.