Momentum cumulants, local equilibrium and stochastic thermostats

We quantitatively investigate the behavior of momentum cumulants in the ϕ4ϕ4 theory under thermal gradients, using stochastic thermostats. We relate this to the violations of local equilibrium. The non-equilibrium behavior is found to be quite well described by a dependence ∼(∇T)2∼(∇T)2, on the temperature gradient. Dependence of the quantities on the thermostat type is analyzed and its physical implications are discussed.