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The energy partitioning during activation and relaxation events understeady-state conditions for a Brownian particle driven by multiple thermalreservoirs of different local temperatures is investigated. Specifically, weapply the formalism derived in a previous article [G. T. Craven and A. Nitzan,J. Chem. Phys. 148, 044101 (2018)] to examine the thermal transport propertiesof two sub-ensembles of Brownian processes, distinguished at any given time bythe specification that all the trajectories in each group have, at that time,energy either above (upside) or below (downside) a preselected energythreshold. Dynamical properties describing energy accumulation and releaseduring activation/relaxation events and relations for upside/downside energypartitioning between thermal reservoirs are derived. The implications for heattransport induced by upside and downside events are discussed.

Upside/Downside statistical mechanics of nonequilibrium Brownian motion. II. Heat transfer and energy partitioning of a free particle