SUPERSPACE SYMMETRY AND THERMODYNAMICS

A thermodynamic criterion is proposed for a generalized symmetry opera tion in condensed matter to be well defined. It is basically the requi rement that the spontaneous break of the defined symmetry should imply a phase transition. This criterion is applied to the rotational symme try in the diffraction diagram of a quasi-periodic system, showing tha t the algebraic structure of the superspace groups is directly derivab le from this physical requirement. Superspace symmetry, as usually def ined in quasi-periodic systems, is the only structural geometrical pro perty yielding rotational diffraction symmetry that is ''stable'' in t he sense that it can only be broken if a phase transition takes place. In contrast, some geometrical configurations producing rotational dif fraction invariances and known as diffraction enhancement of symmetry, , do not fulfil this stability criterion and are expected to happen on ly fortuitously. A physical necessary condition for any generalized sy mmetry in a condensed system is finally conjectured.