Fast Functionalization with High Performance in the Autonomous Information Engine

TL;DR

This paper establishes a speed limit for the relaxation dynamics of an autonomous information heat engine and proposes an optimal initial state inspired by the Mpemba effect to achieve fast functionalization without performance loss.

Contribution

It derives a new speed limit inequality for the relaxation time of the engine and introduces a method to accelerate dynamics using an optimal initial state inspired by the Mpemba effect.

Findings

Speed limit inequality relates relaxation time to state transformation distance.

Optimal initial states can significantly accelerate the engine’s relaxation dynamics.

The approach enables fast functionalization while preserving performance.

Abstract

Mandal and Jarzynski have proposed a fully autonomous information heat engine, consisting of a demon, a mass and a memory register interacting with a thermal reservoir. This device converts thermal energy into mechanical work by writing information to a memory register, or conversely, erasing information by consuming mechanical work. Here, we derive a speed limit inequality between the relaxation time of state transformation and the distance between the initial and final distributions, where the combination of the dynamical activity and entropy production plays an important role. Such inequality provides a hint that a speed-performance trade-off relation exists between the relaxation time to functional state and the average production. To obtain fast functionalization while maintaining the performance, we show that the relaxation dynamics of information heat engine can be accelerated significantly by devising an optimal initial state of the demon. Our design principle is inspired by the so-called Mpemba effect, where water freezes faster when initially heated.