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

Maxwellian ratchets are autonomous, finite-state thermodynamic engines that implement input-output informational transformations. Previous studies of these "demons" focused on how they exploit environmental resources: randomizing ordered inputs, leveraging increased Shannon entropy to transfer energy from a thermal reservoir to a work reservoir. However, to date, correctly determining such functional thermodynamic operating regimes was restricted to engines for which correlations among their information-bearing degrees of freedom could be calculated exactly and in closed form. Additionally, a key second dimension of ratchet behavior was ignored---ratchets do not merely change the randomness of environmental inputs, they construct and deconstruct patterns. To address both dimensions, we adapt recent results from dynamical-systems and ergodic theories that efficiently and accurately calculate the entropy rates and the rate of statistical complexity divergence of general hidden Markov processes. These methods accurately determine thermodynamic operating regime for finite-state Maxwellian demons with arbitrary numbers of states and transitions. The result is a greatly enhanced perspective on the information processing capabilities of information engines.