Gambling Carnot Engine

TL;DR

This paper introduces a theoretical colloidal heat engine that uses a feedback protocol inspired by gambling, enabling full conversion of heat into work and surpassing Carnot efficiency at maximum power.

Contribution

It presents a novel feedback-based model for a heat engine that exceeds traditional efficiency limits using first-passage and martingale theory.

Findings

Engine achieves full heat-to-work conversion.

Surpasses Carnot efficiency at maximum power.

Performance depends on data acquisition rate.

Abstract

We propose a theoretical model for a colloidal heat engine driven by a feedback protocol that is able to fully convert the net heat absorbed by the hot bath into extracted work. The feedback protocol, inspired by gambling strategies, executes a sudden quench at zero work cost when the particle position satisfies a specific first-passage condition. As a result, the engine enhances both power and efficiency with respect to a standard Carnot cycle, surpassing Carnot's efficiency at maximum power. Using first-passage and martingale theory, we derive analytical expressions for the power and efficiency far beyond the quasistatic limit and provide scaling arguments for their dependency with the cycle duration. Numerical simulations are in perfect agreement with our theoretical findings, and illustrate the impact of the data acquisition rate on the engine's performance.