  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. The results are proved under the general setting
of open and non-ideal CRNs.
