Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force

Understand

Recently, it has been shown that there is a trade-off relation between thermodynamic cost and current fluctuations, referred to as the thermodynamic uncertainty relation (TUR).

• The TUR has been derived for various processes, such as discrete-time Markov jump processes and overdamped Langevin dynamics.
• For underdamped dynamics, it has recently been reported that some modification is necessary for application of the TUR.
• In this study, we present a more generalized TUR, applicable to a system driven by a velocity-dependent force in the context of underdamped Langevin dynamics, by extending the theory of Vu and Hasegawa [preprint arXiv:1901.05715].