Uncertainty relations for underdamped Langevin dynamics

Understand

A trade-off between the precision of an arbitrary current and the dissipation, known as the thermodynamic uncertainty relation, has been investigated for various Markovian systems.

• Here, we study the thermodynamic uncertainty relation for underdamped Langevin dynamics.
• By employing information inequalities, we prove that, for such systems, the relative fluctuation of a current at a steady state is constrained by both the entropy production and the average dynamical activity.
• We find that, unlike what is the case for overdamped dynamics, the dynamical activity plays an important role in the bound.