The Thermodynamic Cost of Erasing Information in Finite-time

TL;DR

This paper analyzes the thermodynamic costs of finite-time information erasure using a Brownian particle model, providing analytical tools to evaluate work and its distribution for practical erasure protocols.

Contribution

It introduces a method to compute the full work distribution during finite-time erasure in a double-well potential, extending beyond average work analysis.

Findings

Derived analytical expressions for work in finite-time erasure.

Validated results with numerical simulations.

Provided a framework for practical erasure protocols.

Abstract

The Landauer principle sets a fundamental thermodynamic constraint on the minimum amount of heat that must be dissipated to erase one logical bit of information through a quasi-statically slow protocol. For finite time information erasure, the thermodynamic costs depend on the specific physical realization of the logical memory and how the information is erased. Here we treat the problem within the paradigm of a Brownian particle in a symmetric double-well potential. The two minima represent the two values of a logical bit, 0 and 1, and the particle's position is the current state of the memory. The erasure protocol is realized by applying an external time-dependent tilting force. We derive analytical tools to evaluate the work required to erase a classical bit of information in finite time via an arbitrary continuous erasure protocol, which is a relevant setting for practical applications. Importantly, our method is not restricted to the average work, but instead gives access to the full work distribution arising from many independent realizations of the erasure process. Using the common example of an erasure protocol that changes linearly with time acting on a double-parabolic potential, we explicitly calculate all relevant quantities and verify them numerically.