Hidden collision statistics in bosonic heat transport: Superthermal correlations at fixed mean current

Abstract

Reservoirs with the same mean relaxation rate can be indistinguishable at the level of average energy transport while producing different fluctuations. We study a bosonic mode coupled to hot and cold Poisson streams of thermal ancillas through finite beam-splitter collisions. The averaged evolution is a compound-Poisson semigroup generated by finite Gaussian event channels. Its nonequilibrium steady state is an exact mixture of thermal states governed by a random affine fixed point. Consequently, the mean-occupation dynamics and bath-resolved mean heat currents coincide with those of the matched continuous Lindblad reservoir, whereas higher correlations retain the collision strength. For equal collision transmissivities, we derive an exact superthermal bunching law controlled by the temperature contrast and collision strength. We also obtain the asymptotic rates of the first two heat cumulants for an ideal stationary event-resolved two-point-measurement record and separate local one-collision contributions from temporal correlations. Fock-space diagonalization and Monte Carlo trajectories validate the formulas and connect full resets to the weak-collision Gaussian limit.