Energy balance for a dissipative system

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Abstract
In general, dissipative problems involve both frictional and fluctuation forces. As it turns out, solutions of many of these problems are encompassed by the generalized quantum Langevin equation. Here, we use this equation to obtain a general expression for the work done by the fluctuation force on a quantum particle. At equilibrium, this work is necessary to balance the energy lost by the particle due to the frictional force.