Identifying Functional Thermodynamics in Autonomous Maxwellian Ratchets

TL;DR

This paper introduces a family of Maxwellian Demons with exactly calculable correlations, revealing new thermodynamic functionalities and providing a refined Second Law based on Kolmogorov-Sinai entropy, applicable broadly.

Contribution

The authors develop a new class of Demons with exact correlation calculations, enabling precise thermodynamic analysis and revealing novel functionalities beyond previous models.

Findings

Demons can act as engines or erasers, with some erasing bits by increasing correlations.

Exact correlation calculations lead to tight bounds on Demon performance.

The refined Second Law applies broadly, even when previous bounds are violated.

Abstract

We introduce a family of Maxwellian Demons for which correlations among information bearing degrees of freedom can be calculated exactly and in compact analytical form. This allows one to precisely determine Demon functional thermodynamic operating regimes, when previous methods either misclassify or simply fail due to approximations they invoke. This reveals that these Demons are more functional than previous candidates. They too behave either as engines, lifting a mass against gravity by extracting energy from a single heat reservoir, or as Landauer erasers, consuming external work to remove information from a sequence of binary symbols by decreasing their individual uncertainty. Going beyond these, our Demon exhibits a new functionality that erases bits not by simply decreasing individual-symbol uncertainty, but by increasing inter-bit correlations (that is, by adding temporal order) while increasing single-symbol uncertainty. In all cases, but especially in the new erasure regime, exactly accounting for informational correlations leads to tight bounds on Demon performance, expressed as a refined Second Law of Thermodynamics that relies on the Kolmogorov-Sinai entropy for dynamical processes and not on changes purely in system configurational entropy, as previously employed. We rigorously derive the refined Second Law under minimal assumptions and so it applies quite broadly---for Demons with and without memory and input sequences that are correlated or not. We note that general Maxwellian Demons readily violate previously proposed, alternative such bounds, while the current bound still holds.