Relative entropy in 2D quantum field theory, finite-size corrections, and irreversibility of the renormalization group

The relative entropy in two-dimensional field theory is studied for its application as an irreversible quantity under the renormalization group, relying on a general monotonicity theorem for that quantity previously established. In the cylinder geometry, interpreted as finite-temperature field theory, one can define from the relative entropy a monotonic quantity similar to Zamolodchikov's c function. On the other hand, the one-dimensional quantum thermodynamic entropy also leads to a monotonic quantity, with different properties. The relation of thermodynamic quantities with the complex components of the stress tensor is also established and hence the entropic c theorems are proposed as analogs of Zamolodchikov's c theorem for the cylinder geometry. [S0031-9007(98)07422-5].