Identifying Functional Thermodynamics in Autonomous Maxwellian Ratchets

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. These Demons are as functional as alternative candidates, behaving either as engines, lifting a mass against gravity by extracting energy from a single heat reservoir, or Landauer erasers, removing information from a sequence of binary symbols by consuming external work. In both cases, explicitly 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.