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Maxwellian ratchets are autonomous, finite-state thermodynamic engines thatimplement input-output informational transformations. Previous studies of these"demons" focused on how they exploit environmental resources to generate work:They randomize ordered inputs, leveraging increased Shannon entropy to transferenergy from a thermal reservoir to a work reservoir while respecting bothLiouvillian state-space dynamics and the Second Law. However, to date,correctly determining such functional thermodynamic operating regimes wasrestricted to a very few engines for which correlations among theirinformation-bearing degrees of freedom could be calculated exactly and inclosed form---a highly restricted set. Additionally, a key second dimension ofratchet behavior was largely ignored---ratchets do not merely change therandomness of environmental inputs, their operation constructs and deconstructspatterns. To address both dimensions, we adapt recent results fromdynamical-systems and ergodic theories that efficiently and accuratelycalculate the entropy rates and the rate of statistical complexity divergenceof general hidden Markov processes. In concert with the Information ProcessingSecond Law, these methods accurately determine thermodynamic operating regimesfor finite-state Maxwellian demons with arbitrary numbers of states andtransitions. In addition, they facilitate analyzing structure versus randomnesstrade-offs that a given engine makes. The result is a greatly enhancedperspective on the information processing capabilities of information engines.As an application, we give a thorough-going analysis of the Mandal-Jarzynskiratchet, demonstrating that it has an uncountably-infinite effective statespace.

Functional Thermodynamics of Maxwellian Ratchets: Constructing and Deconstructing Patterns, Randomizing and Derandomizing Behaviors