Universal relations and bounds for fluctuations in quasistatic small heat engines

TL;DR

This paper extends the fundamental thermodynamic bounds to higher-order fluctuations in small heat engines, revealing universal relations dependent only on bath temperatures, and validates these with experimental data.

Contribution

It generalizes Carnot's efficiency bounds to higher moments of work and heat fluctuations in quasistatic small engines, establishing universal bounds and testing them experimentally.

Findings

Higher-order statistics depend only on bath temperature ratios.

Universal bounds for variance ratios of work and heat are derived.

Experimental data from a Brownian Carnot engine support the theory.

Abstract

The efficiency of any heat engine, defined as the ratio of average work output to heat input, is bounded by Carnot's celebrated result. However, this measure is insufficient to characterize the properties of miniaturized heat engines carrying non-negligible fluctuations, and a study of higher-order statistics of their energy exchanges is required. Here, we generalize Carnot's result for reversible cycles to arbitrary order moment of the work and heat fluctuations. Our results show that, in the quasistatic limit, higher-order statistics of a small engine's energetics depend solely on the ratio between the temperatures of the thermal baths. We further prove that our result for the second moment gives universal bounds for the ratio between the variances of work and heat for quasistatic cycles. We test this theory with our previous experimental results of a Brownian Carnot engine and observe the consistency between them, even beyond the quasistatic regime. Our results can be exploited in the design of thermal nanomachines to reduce their fluctuations of work output without marginalizing its average value and efficiency.