Field theory entropy, the [Formula presented] theorem, and the renormalization group

Abstract

We consider entropy and relative entropy in field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization-group fixed points ranks the fixed points, the lowest relative entropy being assigned to the highest multicritical point. We argue that as a consequence of a generalized [Formula presented] theorem Wilsonian RG flows induce an increase in entropy and propose the relative entropy as the natural quantity which increases from one fixed point to another in more than two dimensions. © 1996 The American Physical Society.