Entropic C theorems in free and interacting two-dimensional field theories- art. no. 045006

The relative entropy in two-dimensional field theory is studied on a cylind er geometry, interpreted as finite-temperature field theory. The width of t he cylinder provides an infrared scale that allows us to define a dimension less relative entropy analogous to Zamolodchikov's c function. The one-dime nsional quantum thermodynamic entropy gives rise to another monotonic dimen sionless quantity. I illustrate these monotonicity theorems with examples r anging from free field theories to interacting models soluble with the ther modynamic Bethe ansatz. Both dimensionless entropies are explicitly shown t o be monotonic in the examples that we analyze.