Nonequilibrium Thermodynamics on Ratchets in Brownian Computing in terms of First Passage Time and Entropy Production

Brownian circuits are delay-insensitive circuits that can effectively utilize thermal fluctuations of Brownian particles [1]. In these circuits, thermal noise serves as a resource to drive signals, offering the potential for significantly reduced energy consumption compared to conventional computers. However, the thermodynamic lower limit of the energy consumption on this circuit remains unclear because of its non-equilibrium calculation processes which use the diffusion of Brownian motion. In this study, we aim to elucidate the thermodynamic cost of ratchets, one of the key components of Brownian circuits. Ratchets rectify fluctuating particles and give them a unidirectional motion. They play a critical role not only in increasing computational speed but also in terminating computation and erasing information. We consider a one-dimensional random walk model and derive the first passage time of a Brownian particle for each ratchet performance. We show that ratchets exhibit varying first passage times depending on their positioning even for the same ratchet performance. Our presentation provides a detailed account of the performance and positional dependencies of ratchets in terms of entropy production.

[1]J. Lee, F. Peper, S. Cotofana, M. Naruse, M. Ohtsu, T. Kawazoe, Y. Takahashi, T. Shimokawa, L. Kish, T. Kubota, Int. Journ. of Unconventional Computing, 12, 341 (2016).