Inferring dissipation from the violation of Fluctuation-Dissipation Theorem for Markov systems

Shou-Wen Wang

Published 2017-10-28Version 1

The Harada-Sasa equality elegantly connects the dissipation of a moving object with its measurable violation of the Fluctuation-Dissipation Theorem (FDT). Although proven for Langevin processes, its application to Markov processes has remained unclear, especially when the local dissipation contributes asymmetrically to the forward and backward transitions. Here, we show that, while the FDT violation persists surprisingly in the high frequency limit due to this asymmetry, the Harada-Sasa equality is restored by neglecting this high frequency violation, and furthermore, by assuming that not only the dissipation per jump is small, as compared to the thermal energy unit, but also its variation along the observed direction. In fact, these assumptions lead to an effective Langevin dynamics, thus rationalizing the result. The symmetric case is unique, as it has a much smaller deviation from the Harada-Sasa equality, thus allowing for larger discreteness.