Year: 2022
Type: article
Abstract: Landauer's principle imposes a fundamental limit on the energy cost to perfectly initialize a classical bit, which is only reached under the ideal operation with infinitely long time. The question on the cost in the practical operation for a bit has been raised under the constraint by the finiteness of operation time. We discover a raise-up of energy cost by ${\mathcal{L}}^{2}(\ensuremath{\epsilon})/\ensuremath{\tau}$ from the Landaeur's limit (${k}_{B}Tln2$) for a finite-time $\ensuremath{\tau}$ initialization of a bit with an error probability $\ensuremath{\epsilon}$. The thermodynamic length $\mathcal{L}(\ensuremath{\epsilon})$ between the states before and after initializing in the parametric space increases monotonously as the error decreases. For example, in the constant dissipation coefficient (${\ensuremath{\gamma}}_{0}$) case, the minimal additional cost is $0.997{k}_{B}T/({\ensuremath{\gamma}}_{0}\ensuremath{\tau})$ for $\ensuremath{\epsilon}=1%$ and $1.288{k}_{B}T/({\ensuremath{\gamma}}_{0}\ensuremath{\tau})$ for $\ensuremath{\epsilon}=0.1%$. Furthermore, the optimal protocol to reach the bound of minimal energy cost is proposed for the bit initialization realized via a finite-time isothermal process.
Source: Physical review. E
Authors: Yu-Han Ma, Jin-Fu Chen, C. P. Sun, Hui Dong
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4295862267