Speeding Up Classical and Quantum Adiabatic Processes: Implications for Work Functions and Heat Engine Designs

TL;DR

This paper presents methods to accelerate classical and quantum adiabatic processes using control protocols, reducing work fluctuations and enhancing the performance of heat engines and the convergence of thermodynamic relations.

Contribution

It introduces a unified approach to fast-forward adiabatic processes in classical and quantum systems, improving efficiency and power output.

Findings

Significant reduction in work fluctuation during fast-forward adiabatic processes

Enhanced convergence rate of the Jarzynski equality with fast-forward protocols

Improved efficiency and power output of quantum heat engines

Abstract

Adiabatic processes are important for studying the dynamics of a time-dependent system. Conventionally, the adiabatic processes can only be achieved by varying the system slowly. We speed up both classical and quantum adiabatic processes by adding control protocols. In classical systems, we work out the control protocols by analyzing the classical adiabatic approximation. In quantum systems, we follow the idea of transitionless driving by Berry [J. Phys. A: Math. Theor. Vol.42 365303 (2009)]. Such fast-forward adiabatic processes can be performed at arbitrary fast speed, and in the meanwhile reduce the work fluctuation. In both systems, we use a time-dependent harmonic oscillator model to work out explicitly the work function and the work fluctuation in three types of processes: fast-forward adiabatic processes, adiabatic processes, and non-adiabatic processes. We show the significant reduction on work fluctuation in fast-forward adiabatic process. We further illustrate how the fast-forward process improved the converging rate of the Jarzynski equality between the work function and the free energy. As an application, we show that the fast-forward process not only maximizes the output power but also improve the efficiency of a quantum engine.