Detailed Jarzynski Equality applied on a Logically Irreversible Procedure

TL;DR

This paper demonstrates that a detailed Jarzynski equality can accurately determine Landauer's bound in a single-bit memory erasure process regardless of speed, by analyzing subprocesses with a Brownian particle in a double-well potential.

Contribution

It applies a detailed Jarzynski equality to a logically irreversible memory erasure process, providing a method to determine Landauer's bound independent of erasure speed.

Findings

The minimum work approaches Landauer's bound only at slow erasure speeds.

A detailed Jarzynski equality accurately predicts Landauer's bound regardless of erasure speed.

Generalized Jarzynski equality relates work to return probabilities in subprocesses.

Abstract

A single bit memory system is made with a brownian particle held by an optical tweezer in a double-well potential and the work necessary to erase the memory is measured. We show that the minimum of this work is close to the Landauer's bound only for very slow erasure procedure. Instead a detailed Jarzynski equality allows us to retrieve the Landauer's bound independently on the speed of this erasure procedure. For the two separated subprocesses, i.e. the transition from state 1 to state 0 and the transition from state 0 to state 0, the Jarzynski equality does not hold but the generalized version links the work done on the system to the probability that it returns to its initial state under the time-reversed procedure.