Conditional entropy and Landauer principle

TL;DR

This paper investigates the role of conditional entropy in the Landauer principle, showing it can be nonzero in symmetric bistable systems and affects the minimum heat produced during information processing.

Contribution

It demonstrates that conditional entropy can be nonzero in symmetric bistable systems and decomposes it into three probabilistic terms, expanding understanding of heat limits in computation.

Findings

Conditional entropy can be nonzero in symmetric bistable systems.

Conditional entropy can be expressed as the sum of three probabilistic terms.

The contribution of these terms affects the minimum heat in bit-reset operations.

Abstract

Landauer principle describes the minimum heat produced by an information-processing device. Recently a new term has been included in the minimum heat production: it's called conditional entropy and takes into account the microstates content of a given logic state. Usually this term is assumed zero in bistable symmetric systems thanks to the strong hypothesis used to derive Landauer principle. In this paper we show that conditional entropy can be nonzero even for bistable symmetric systems and that it can be expressed as the sum of three different terms related to the probabilistic features of the device. The contribution of the three terms to conditional entropy (and thus to minimum heat production) is then discussed for the case of bit-reset.