Abstract
In this paper, we explore the conservation-dissipation structure and balance equations for linear systems forced with white noise process. The proposed methodology bases on a Fokker-Planck operator with the analytic expression and an operator decomposition. The symmetric component accounts for a conservative dynamics and the skew-symmetric corresponds to a dissipating system. In terms of an important structural condition, the dissipation structures are correlated with the stationary equilibrium states, while the conservation structures are correlated with the stationary non-equilibrium states. We also conduct the energy and entropy flow analysis in the non-equilibrium circumstance associated with unbalanced probability circulation. Finally, the framework enables us to evidence the First and Second Law of thermodynamics by relating the dissipativity theory to entropy production, heat dissipation, and work extraction.
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