First and Second Laws of Information Processing

Autonomous Maxwellian ratchets are Maxwellian demons which can explicitly leverage correlations among information-bearing degrees of freedom to exchange thermodynamic resources—for example, to extract heat from a single bath and convert it to work, at the cost of modifying the values in a data tape. Previous studies have bounded this behavior in a variety of circumstances, deriving “information processing second laws” for the ratchet’s functionality.

The steady-state surprisal of stochastic thermodynamics provides another concrete link between a ratchet's information-bearing and thermodynamic structure. By considering its average change (and rate thereof) under a given process, we uncover an information processing first law that extends—to strict equalities—various information processing second laws. We then show how stochastic thermodynamics’ integral fluctuation theorems take the first law equality to second law inequalities, thus recovering, extending, and ultimately tightening previous results for nonequilibrium steady-state ratchets which violate detailed balance—the case for a great number of complex biological and biophysical processes.

In this talk, we will present the information processing first and second laws and then apply them to an example ratchet designed to tunably violate detailed balance in its effective dynamics. This explicates the quantitative and qualitative effects of nonequilibrium steady states on ratchet thermodynamics, and so further elucidates how such systems exchange energy and information to function.