Geodesic path for the minimal energy cost in shortcuts to isothermality

TL;DR

This paper establishes a universal method for designing energy-efficient control schemes in shortcuts to isothermality by linking the problem to finding geodesic paths in control parameter space, demonstrated with a Brownian particle example.

Contribution

It proves the equivalence between optimal control design and geodesic path finding, providing a systematic approach to minimize energy costs in finite-time thermodynamic processes.

Findings

The method effectively reduces energy costs in control schemes.

Application to a Brownian particle demonstrates practical utility.

Provides a universal framework for optimal control in thermodynamics.

Abstract

Shortcut to isothermality is a driving strategy to steer the system to its equilibrium states within finite time, and enables evaluating the impact of a control promptly. Finding optimal scheme to minimize the energy cost is of critical importance in applications of this strategy in pharmaceutical drug test, biological selection, and quantum computation. We prove the equivalence between designing the optimal scheme and finding the geodesic path in the space of control parameters. Such equivalence allows a systematic and universal approach to find the optimal control to reduce the energy cost. We demonstrate the current method with examples of a Brownian particle trapped in controllable harmonic potentials.