Comment on "Validity of path thermodynamic description of reactive systems: Microscopic simulations''

Abstract

The claims by Baras, Garcia, and Malek Mansour [Phys. Rev. E 107, 014106 (2023)] on the validity of path thermodynamics are ill founded and contradict well known results. Following up on a previous comment, I show that, for both models of chemical reaction networks considered in the aforementioned paper, path thermodynamics yields values of the entropy production rates fully consistent with those expected from standard chemical thermodynamics in the large-system limit.

Figures (1)

• Figure 1: Entropy production rate (EPR $=d_{\rm i}S/dt$) versus $a^2$ for model $0$ (open circles), model I (open diamonds), and model II (open squares) computed with the stochastic method using Eq. (\ref{['EPR-stoch']}). The pluses joined by the solid lines give the expectation (\ref{['EPR-thermo']}) from standard macroscopic thermodynamics. The extensivity parameter is equal to $\Omega=10^4$ and the total time interval to compute the EPR is taken as $t=10^4$. For model I, the parameter values are $k_{+1}=k_{-1}=1$, $k_{+2}=k_{-2}=5/6$, $b=6a/5$, $c=a/2$, the steady state is $x_s=a/\sqrt{2}$, and the expected entropy production rate (\ref{['EPR-thermo']}) is given by $k_{\rm B}^{-1}{\rm EPR}_{\rm th}=(\Omega/2)a^2(\sqrt{2}-1)\ln 2\simeq 0.14356\, a^2 \Omega$. For model II, they are $k_{+1}=k_{-1}=k_{+2}=k_{-2}=1$, $a=1$, $b=5a/3$, $c=a/3$, $x_s=a(\sqrt{209}-5)/12$, and $k_{\rm B}^{-1}{\rm EPR}_{\rm th}=\Omega(a^2-x_s^2)\ln 9\simeq 0.83263\, a^2 \Omega$. For model $0$, the parameter values and the steady state are the same as for model I, but ${\rm EPR}_{\rm th}=0$. The mean accuracy $k_{\rm B}^{-1}\langle\vert{\rm EPR}_{\rm num}-{\rm EPR}_{\rm th}\vert\rangle$ is equal to $3\times 10^{-6}$, $0.75$, and $2.6$ for models $0$, I, and II, respectively. The Hill-Schnakenberg graphs of the models are shown as insets.