Landauer Bound for Analog Computing Systems

TL;DR

This paper extends the Landauer bound to analog computing systems, showing that entropy production during information erasure is related to the configurational volume, thus limiting infinite precision due to fundamental physical laws.

Contribution

It generalizes the Landauer bound to continuous variables, linking information erasure to phase transitions and establishing fundamental energy limits for analog computation.

Findings

Entropy production per degree of freedom equals the logarithm of the configurational volume.

Infinite precision in analog computing is physically impossible due to energy constraints.

Every computation must operate with a finite number of bits, preventing infinite accuracy.

Abstract

By establishing a relation between information erasure and continuous phase transitions we generalise the Landauer bound to analog computing systems. The entropy production per degree of freedom during erasure of an analog variable (reset to standard value) is given by the logarithm of the configurational volume measured in units of its minimal quantum. As a consequence every computation has to be carried on with a finite number of bits and infinite precision is forbidden by the fundamental laws of physics, since it would require an infinite amount of energy.