The nonperturbative functional renormalization group and its applications

The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilson's RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity.Comment: v2) Review article, 93 pages + bibliography, 35 figure

Phenomenological thermodynamics V: the 2nd law applied to extensive functional with the use of Lagrange multipliers

In most of our preceding articles (I-IV), we split the 2nd law into two parts: a) the law of evolution of an adiabatically isolated system Σ (= Σo), and b) the law of equilibrium of an isolated Σ (= Σoo). This article is mainly devoted to the 2nd law part b, where we demonstrate that the maximum of the entropy functional S[. . .] may be found by the use of Lagrange multipliers expressing the conservation of the energy functional H[. . .] and, in general, of several other conserved extensive quantities.</p