Functional Thermodynamics for Arbitrary Mawellian Ratchets

Autonomous Maxwellian demons use structured environments as a resource to generate work by randomizing ordered inputs and leveraging the increased Shannon entropy to transfer energy from a thermal reservoir to a work reservoir. To date, determining their functional thermodynamic operating regimes was restricted to information engines for which correlations among information-bearing degrees of freedom can be calculated exactly via compact analytical forms - a highly restricted set of engines. Although information engines may be represented as finite hidden Markov chains, (i) no finite expression for their Shannon entropy rate exists, (ii) the set of their predictive features is generically uncountably infinite, and (iii) their statistical complexity diverges. To solve the problems these pose, we adapt recent results from dynamical systems theory to efficiently and accurately calculate the entropy rates and the rate of statistical complexity divergence of general hidden Markov chains. The results allow for precise determination of the thermodynamic functionality of previously-studied Maxwellian demons, as well as greatly expand the class of analyzable information engines.