Thermodynamics of Feedback with application to Landauer's Principle

Measurement and feedback are integral components for efficient functioning of physical systems in the microscopic as well as macroscopic world. We will analyze and quantify the thermodynamic costs of performing bit level measurements and energetics of feedback action. The thermodynamic system of interest studied is a Brownian particle in a bi-stable well, which is often used as a model for a single bit memory in the study of erasure of information. Landauer states that the minimum amount of heat dissipation for erasing a memory bit is k_BTln2, which provides the Landauer limit. Recent experiments demonstrate that the erasure can be achieved with energetics close to the Landauer's bound. The protocols in prior art are open-loop, where the information on the state of the memory is not employed in the erasure protocol. Here, we quantify the energetics of erasure protocols with feedback; experimentally as well as via Monte Carlo simulations. Results indicate that the deficit between the heat dissipation in the feedback based erasure protocol and the k_BTln 2 can be accounted for quantitatively by the measurement and feedback mechanisms. Non-conservative bounds are obtained on the deficit.