Large deviations of energy transfers in nonequilibrium CFT and asymptotics of non-local Riemann–Hilbert problems

A wide class of $$1+1$$ dimensional unitary conformal field theories allows for an explicit construction nonequilibrium “profile states” interpolating smoothly between different equilibria on the left and right. It has been recently established that generating function full counting statistics energy transfers in such states may be expressed terms solution to a non-local Riemann–Hilbert problem. Following earlier works transfers, particular ones Bernard–Doyon “partitioning protocol” theory, profile was conjectured satisfy large deviation principle limit long transfer-times. The present paper establishes rigorously this conjecture by carrying out long-time asymptotic analysis underlying