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.

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. D

References in corpus (6)

• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Renormalization Group Patterns and C-Theorem in More Than Two Dimensions
• Environmentally Friendly Renormalization
• Free energy decreases along Wilson renormalization group trajectories
• Quantum Fluctuations and Irreversibility

Cited by in corpus (28)

• A finite entanglement entropy and the c-theorem
• Mutual Information, Neural Networks and the Renormalization Group
• Is Our Universe Natural?
• Emergence in Holographic Scenarios for Gravity
• The Information Geometry of the Spherical Model
• Can Renormalization Group Flow End in a Big Mess?
• Information geometric approach to the renormalisation group
• The Information Geometry of the One-Dimensional Potts Model
• The Information Geometry of the Ising Model on Planar Random Graphs
• The renormalisation group via statistical inference
• Renormalization Group Flow as Optimal Transport
• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model
• Optimal Renormalization Group Transformation from Information Theory
• C Function Representation of the Local Potential Approximation
• Relevance in the Renormalization Group and in Information Theory
• Relative entropy in 2d Quantum Field Theory, finite-size corrections and irreversibility of the Renormalization Group
• Renormalisation Group Flow and Geodesics in the O(N) Model for Large N
• Entropic C-theorems in free and interacting two-dimensional field theories
• Entropy constraints on effective field theory
• Renormalization group irreversible functions in more than two dimensions
• Stochastic formulation of the renormalization group: supersymmetric structure and topology of the space of couplings
• A Statistical Fields Theory underlying the Thermodynamics of Ricci Flow and Gravity
• Small numerators canceling small denominators of the high-temperature scaling variables: a systematic explanation in arbitrary dimensions
• Relative entropy for compact Riemann surfaces
• Renormalization Group and Quantum Information
• Relative Entropy and Mutual Information in Gaussian Statistical Field Theory
• Chaotic renormalization group flow and entropy gradients over Haros graphs
• Minimizing couplings in renormalization by preserving short-range mutual information