Identifying functional thermodynamics in autonomous Maxwellian ratchets
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 individualsymbol uncertainty, but by increasing interbit correlations (that is, by adding temporal order) while increasing singlesymbol 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 KolmogorovSinai 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. As such, it broadly describes the minimal energetic cost of any computation by a thermodynamic system.
 Publication:

New Journal of Physics
 Pub Date:
 February 2016
 DOI:
 10.1088/13672630/18/2/023049
 arXiv:
 arXiv:1507.01537
 Bibcode:
 2016NJPh...18b3049B
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematics  Dynamical Systems;
 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Biological Physics;
 Physics  Chemical Physics
 EPrint:
 13 pages, 9 figures, http://csc.ucdavis.edu/~cmg/compmech/pubs/mrd.htm