LMP Seminar: Direct proof of Thermodynamics Uncertainty Relations

Thermodynamic uncertainty relations (TURs) bound the dissipation in non-equilibrium systems from below by the fluctuations of an observed current. In contrast to the elaborate and indirect techniques employed in existing proofs of TURs, we prove them directly from the Langevin equation using stochastic calculus. This finally establishes the TUR as an inherent property of overdamped stochastic equations of motion, akin to quantum-mechanical uncertainty. The direct proof allows us to extend the transient TUR to currents and densities with explicit time-dependence, and by including current-density correlations we derive a new sharpened TUR for transient dynamics. In the talk I will present and explain the new direct proof of TURs.
[1] C. Dieball & AG, Phys. Rev. Lett. 130, 087101 (2023)