[Paper Review] Role of conditional entropy in experimental tests of Landauer Principle

Davide Chiuchiú, M. C. Diamantini+1 more|arXiv (Cornell University)|Jun 10, 2014

Advanced Thermodynamics and Statistical Mechanics2 citations

TL;DR

This paper re-evaluates Landauer's principle by demonstrating that conditional entropy—previously assumed zero in symmetric bistable systems—can be nonzero due to probabilistic microstate distributions. For bit-reset, it decomposes conditional entropy into three distinct terms, showing their contributions to minimum heat production and challenging the standard assumption of negligible information-theoretic effects in symmetric devices.

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.

Motivation & Objective

• To challenge the conventional assumption that conditional entropy is zero in symmetric bistable systems.
• To identify and quantify the probabilistic components contributing to conditional entropy in such systems.
• To analyze how these components influence the minimum heat production during bit-reset operations.
• To provide a refined theoretical framework for Landauer's principle incorporating non-zero conditional entropy.

Proposed method

• Derives conditional entropy as a sum of three distinct terms based on the probabilistic features of the system's microstates.
• Applies information-theoretic formalism to model the joint and conditional probabilities of device states and their microstates.
• Uses statistical mechanics to express heat production in terms of conditional entropy, extending Landauer's original formulation.
• Analyzes the bit-reset process to isolate and evaluate the contributions of each term to minimum heat.
• Considers symmetric bistable systems under general probabilistic assumptions, avoiding the strong symmetry hypotheses that previously set conditional entropy to zero.

Experimental results

Research questions

• RQ1 Can conditional entropy be non-zero in symmetric bistable systems, contrary to standard assumptions?
• RQ2 What are the three distinct probabilistic components that contribute to conditional entropy in such systems?
• RQ3 How do these components affect the minimum heat production during a bit-reset operation?
• RQ4 To what extent does the inclusion of conditional entropy alter the predictions of Landauer's principle?

Key findings

• Conditional entropy is not necessarily zero in symmetric bistable systems, even under standard assumptions, due to non-uniform microstate distributions.
• The conditional entropy decomposes into three distinct terms, each reflecting different probabilistic features of the device's state space.
• For bit-reset, these three terms collectively determine the minimum heat production, with measurable contributions from each component.
• The paper demonstrates that the standard Landauer bound can be exceeded when conditional entropy is non-zero, challenging the universality of the zero-conditional-entropy assumption.