Information processing second law for an information ratchet with finite tape

Abstract

We model a class of discrete-time information ratchet with a finite tape and explore its thermodynamic consequence as a Maxwell demon. We found that, although it supports the operational regime of an engine or eraser, it cannot typically sustain these thermodynamic functionalities due to eventual equilibration as a result of the finite information capacity of the tape. Nonetheless, cumulative work can be accrued or expended through successive tape scans and we prove that at all time the ratchet obeys the information processing second law (IPSL). Unlike the IPSL for the infinite-tape ratchet which operates only at the stationary state, the IPSL here is applicable also at the transient phase of the ratchet operation. We explore two ratchet designs with the single-state perturbed coin (PC) ratchet being the simplest ratchet without memory, while the double-state modified Boyd's (MB) ratchet is the simplest ratchet with memory. Our analysis shows that the MB ratchet can harness correlation to accumulate more work by having a larger time constant to reach steady state relative to the PC ratchet.