Fluctuations in Single-Shot $\epsilon$-Deterministic Work Extraction

TL;DR

This paper develops a fluctuation relation tailored for single-shot epsilon-deterministic work extraction, addressing the fluctuations caused by small failure probabilities in finite-time microscopic processes, and generalizes existing bounds.

Contribution

It introduces a new fluctuation relation specific to single-shot epsilon-deterministic work extraction, extending the theoretical framework to include continuous heat bath contact.

Findings

Formulated and proved a fluctuation relation for single-shot work extraction.

Derived bounds on epsilon-deterministic work as a corollary.

Allowed the system to be in contact with a heat bath at all times.

Abstract

There has been an increasing interest in the quantification of nearly deterministic work extraction from a finite number of copies of microscopic particles in finite time. This paradigm, so called single-shot epsilon-deterministic work extraction, considers processes with small failure probabilities. However, the resulting fluctuations in the extracted work entailed by this failure probability have not been studied before. In the standard thermodynamics paradigm fluctuation theorems are powerful tools to study fluctuating quantities. Given that standard fluctuation theorems are inadequate for a single-shot scenario, here we formulate and prove a fluctuation relation specific to the single-shot epsilon-deterministic work extraction to bridge this gap. Our results are general in the sense that we allow the system to be in contact with the heat bath at all times. As a corollary of our theorem we derive the known bounds on the epsilon-deterministic work.