Equivalence of Discrete and Continuous Otto-Like Engines assisted by Catalysts: Mapping Catalytic Advantages from the Discrete to the Continuous Framework

TL;DR

This paper establishes a theoretical equivalence between discrete and continuous Otto-like engines with catalysts, enabling the transfer of catalytic advantages from discrete models to more experimentally feasible continuous systems.

Contribution

It introduces a mapping framework that connects discrete catalytic engines to continuous ones, facilitating experimental realization of catalytic enhancements.

Findings

Catalytic enhancement observed in continuous Otto engines.

Mapping discrete processes onto continuous models.

Theoretical demonstration of equivalence between engine types.

Abstract

The catalytic extension of a discrete two-stroke engine employs a cyclic auxiliary system - the catalyst - that remains decoupled from the baths and performs no work, yet enhances power and efficiency beyond the corresponding non-catalytic counterpart. Theoretical models of discrete engines are relatively easy to analyze but remain challenging for experimental implementation due to the required control over individual strokes. In contrast, externally driven engines that are simultaneously coupled to both heat baths - the so-called continuous engines - are more experimentally feasible. Here, we establish an equivalence between discrete and continuous machines, both with and without a catalyst, by mapping the discrete unitary processes and thermalization steps onto an interaction Hamiltonian and a Markovian model of dissipation. As a result, by replacing probability flows with probability currents, we construct an analogous continuous machine corresponding to previously demonstrated catalytic schemes that generalize Otto engines. We illustrate this mapping for the simplest catalytic extension of the Otto engine, demonstrating catalytic enhancement in the continuous regime.