On the validity of the thermodynamic uncertainty relation in quantum systems

Understand

We examine the so-called thermodynamic uncertainty relation (TUR), a cost-precision trade-off relationship in transport systems.

• Based on the fluctuation symmetry, we derive a condition on the validity of the TUR for general nonequilibrium (classical and quantum) systems.
• We find that the first non-zero contribution to the TUR beyond equilibrium, given in terms of nonlinear transport coefficients, can be positive or negative, thus affirming or violating the TUR depending on the details of the system.
• We exemplify our results for noninteracting quantum systems by deriving the thermodynamic uncertainty relation in the language of the transmission function.