Thermodynamic uncertainty relation and thermodynamic speed limit in deterministic chemical reaction networks

Kohei Yoshimura, Sosuke Ito

Published 2021-04-30Version 1

We generalize thermodynamic uncertainty relation (TUR) and thermodynamic speed limit (TSL) for deterministic chemical reaction networks (CRNs). The scaled diffusion coefficient derived by considering the connection between macroscopic CRNs and mesoscopic CRNs plays an essential role in our results. The TUR shows that the product of the entropy production rate and the ratio of the scaled diffusion coefficient to the square of the rate of concentration change is bounded below by 2. The TSL states a trade-off relation between speed and thermodynamic quantities, the entropy production and the time-averaged scaled diffusion coefficient. Because we only postulate a relationship between kinetics and thermodynamics called the weak detailed balance condition, the results are so general that they hold in open and non-ideal CRNs.