Universal bounds on fluctuations for machines with broken time-reversal symmetry

TL;DR

This paper derives universal bounds on the fluctuations of output currents relative to input currents in machines with broken time-reversal symmetry, applicable to quantum and classical heat engines, linking to thermodynamic uncertainty relations.

Contribution

It establishes universal bounds on current fluctuations in systems with broken time-reversal symmetry, connecting these bounds to generalized thermodynamic uncertainty relations.

Findings

Bound on relative fluctuation of output currents is lower than that of input currents.

Universal upper and lower bounds for fluctuation ratios are derived.

Results are demonstrated on quantum thermoelectric and classical Brownian heat engines.

Abstract

For a generic class of machines with broken time-reversal symmetry we show that in the linear response regime the relative fluctuation of the sum of output currents for time-forward and time-reversed processes is always lower bounded by the corresponding relative fluctuation of the sum of input currents. This bound is received when the same operating condition, for example, engine, refrigerator or pump, is imposed in both the forward and the reversed processes. As a consequence, universal upper and lower bounds for the ratio of fluctuations between the output and the input current is obtained. Furthermore, we establish an important connection between our results and the recently obtained generalized thermodynamic uncertainty relation for time-reversal symmetry broken systems. We illustrate these findings for two different types of machines: (i) a steady-state three-terminal quantum thermoelectric setup in presence of an external magnetic field, and (ii) a periodically driven classical Brownian heat engine.