We study classical heat conduction in a dissipative open system composed of interacting oscillators. By exactly solving a twisted Fokker-Planck equation which describes the full counting statistics of heat flux flowing through the system, we identify the geometric-phase-like effect and examine its impact on the classical heat transport. We find that the nonlinear interaction as well as the closely related temperature dependence of system parameters are crucial in manifesting the geometric-phase contribution of heat flux. Finally, we propose an electronic experiment based on RC circuits to verify our theoretical predictions.
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