Theory of Critical Fluctuations

A macroscopic system is subdivided into cells of identical size and shape arranged in a regular spatial array. The method of canonical ensembles would consider one of the cells, schematizing the rest into a "reservoir." The present "cellular method" treats the cells on an equal footing and is appropriate to deal with the fluctuations near the critical point for which the standard theory yields infinite results. Earlier theories dealing with the same problem appear as special cases of the present treatment. In particular, the critical points are defined generally enough to include the so-called $\lambda$-points in solids. The macroscopic system is invariant under the group of translations which displaces one cell into another. The macroscopic quantities (e.g., the thermodynamic parameters) are invariants of this group.