Universal Bounds on Fluctuations in Continuous Thermal Machines

TL;DR

This paper establishes fundamental bounds on the fluctuations of steady-state continuous thermal machines, linking their precision to efficiency and Carnot limits, with implications across various operational regimes.

Contribution

It provides universal bounds on fluctuation ratios in thermal machines, extending beyond linear response and applicable to different engine types.

Findings

Relative fluctuations of output are bounded by input fluctuations.

Bounds depend on the engine's efficiency and Carnot efficiency.

Tight-coupling limit saturates the lower bound.

Abstract

We study bounds on ratios of fluctuations in steady-state time-reversal heat engines controlled by multi affinities. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower-bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.