Energy current cumulants in one-dimensional systems in equilibrium

Recently a remarkable connection has been proposed between the fluctuating hydrodynamic equations of a one-dimensional fluid and the Kardar-Parizi-Zhang (KPZ) equation for interface growth. This connection has been used to relate equilibrium correlation functions of the fluid to KPZ correlation functions. Here we use this connection to compute the exact cumulant generating function for energy current in the fluid system. This leads to exact expressions for all cumulants and in particular to universal results for certain combinations of the cumulants. As examples, we consider two different systems which are expected to be in different universality classes, namely a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Simulations provide excellent confirmation of our theory.