The methods of statistical physics are exemplified in the classical perfect gas-each atom is a single dynamical entity. Such methods can be applied in ecology to the distribution of cosmopolitan species over many sites. The analogue of an atom is a class of species distinguished by the number of sites at which it occurs, hardly a material entity; yet, the methods of statistical physics nonetheless seem applicable. This paper compares the application of statistical mechanics to the distribution of atoms and to the vastly different problem of distribution of cosmopolitan species. A number of different approaches show that these distributed entities must be in some sense equivalent; the dynamics must be controlled by interaction between species and the global environment rather than between species and many uncorrelated local environments.
Keywords: alien species distributions; statistical mechanics; stochastic processes.