Aspects of entropy functionals and monotonicity along a RG flow

In this talk, I will motivate our goal of understanding monotonicity of RG flow for n-dimensional spacetimes within the framework of nonequilibrium thermodynamics. We first motivate our construction with a simple toy example. Drawing similarity between RG flow equations and Langevin equations with random noise fluctuations, we construct a path-integral description for the motion of a single diffusive particle and define a path-dependent microscopic entropy functional. Also taking into account environment entropy, we eventually demonstrate a monotonicity condition for total entropy. I will then apply a similar technique to 2dimensional sigma model and look at the low-energy sector —effectively described by a dual target space theory. Following techniques pioneered by Perelman, we will also introduced a macroscopic entropy functional analogous to Perelman entropy functional and study its growth rate. Eventually, we will demonstrate a monotonicity for the effective low-energy description of such NLSMs thus generalizing the c-theorem for a significantly large class of string theories.