Field Theory Entropy, the $H$-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 $H$ 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.Comment: 25 pages, plain TeX (macros included), 6 ps figures. Addition in title. Entropy of cutoff Gaussian model modified in section 4 to avoid a divergence. Therefore, last figure modified. Other minor changes to improve readability. Version to appear in Phys. Rev.