Definition of chemical equilibrium According to the definition of chemical equilibrium in Wikipedia, it is a situation where the rate of the forward reaction is same as the rate of backward reaction and the concentrations of the reactants and the products do not change with time. I hope that the same definition applies to particle physics processes such as a 2-2 scattering of the form $A+B\leftrightarrow C+D$ i.e., in chemical equilibrium concentrations or number densities of each particle species remains unchanged with time.

Consistency of the definition with Boltzmann equation Boltzmann equation is used to study baryogenesis, relic abundance of dark matter and so on. According to Boltzmann equation, the number density $n$ of the species $A$ in an expanding Universe changes as: $$\frac{dn}{dt}+3Hn=\int d\pi_A d\pi_B d\pi_C d\pi_D[f_Af_B|\mathcal{M}|^2_{AB\to CD}+f_Cf_D|\mathcal{M}|^2_{CD\to AB}]$$ where $\mathcal{M}_{AB\to CD}$ and $\mathcal{M}_{CD\to AB}$ are the amplitudes of the forward and backward processes respectively, $H$ is the Hubble parameter. $d\pi_i$ and $f_i$ ($i=A,B,C,D$) are respectively the integrals over phase space and phase space distributions. Due to the $+$ sign on the RHS, the RHS is nonzero in chemical equilibrium even when $$\mathcal{M}_{AB\to CD}=\mathcal{M}_{CD\to AB},~\text{(assuming CP or T invariance)}$$ Therefore, $$\frac{dn}{dt}+3Hn\neq 0.$$ Therefore, the number density of species $A$ can change with time even when the dilution due to expansion is zero i.e., $H=0$. Therefore, the number density or the concentration of $A$ changes in even in chemical equilibrium.

Question Shouldn't the RHS of the Boltzmann equation be zero in chemical equilibrium in order to keep the concentration of each species unchanged with time?

Definition of chemical equilibrium According to the definition of chemical equilibrium in Wikipedia, it is a situation where the rate of the forward reaction is same as the rate of backward reaction and the concentrations of the reactants and the products do not change with time. I hope that the same definition applies to particle physics processes such as a 2-2 scattering of the form $A+B\leftrightarrow C+D$ i.e., in chemical equilibrium concentrations or number densities of each particle species remains unchanged with time.

Consistency of the definition with Boltzmann equation Boltzmann equation is used to study baryogenesis, relic abundance of dark matter and so on. According to Boltzmann equation, the number density $n$ of the species $A$ in an expanding Universe changes as: $$\frac{dn}{dt}+3Hn=\int d\pi_A d\pi_B d\pi_C d\pi_D[f_Af_B|\mathcal{M}|^2_{AB\to CD}+f_Cf_D|\mathcal{M}|^2_{CD\to AB}]$$ where $\mathcal{M}_{AB\to CD}$ and $\mathcal{M}_{CD\to AB}$ are the amplitudes of the forward and backward processes respectively, $H$ is the Hubble parameter defined as $H=\frac{\dot{a}}{a}$ where $a$ is the exapsnion factor. $d\pi_i$ and $f_i$ ($i=A,B,C,D$) are respectively the integrals over phase space and phase space distributions. Due to the $+$ sign on the RHS, the RHS is nonzero in chemical equilibrium even when $$\mathcal{M}_{AB\to CD}=\mathcal{M}_{CD\to AB},~\text{(assuming CP or T invariance)}$$ Therefore, $$\frac{dn}{dt}+3Hn\neq 0.$$ Therefore, the number density of species $A$ can change with time even when the dilution due to expansion is zero i.e., $H=0$. Therefore, the number density or the concentration of $A$ changes in even in chemical equilibrium.

Question Shouldn't the RHS of the Boltzmann equation be zero in chemical equilibrium in order to keep the concentration of each species unchanged with time?

Definition of chemical equilibrium According to the definition of chemical equilibrium in Wikipedia, it is a situation where the rate of the forward reaction is same as the rate of backward reaction and the concentrations of the reactants and the products do not change with time. I hope that the same definition applies to particle physics processes such as a 2-2 scattering of the form $A+B\leftrightarrow C+D$ i.e., in chemical equilibrium concentrations or number densities of each particle species remains unchanged with time.

Consistency of the definition with Boltzmann equation According to Boltzmann equation, the number density $n$ of the species $A$ in an expanding Universe changes as: $$\frac{dn}{dt}+3Hn=\int d\pi_A d\pi_B d\pi_C d\pi_D[f_Af_B|\mathcal{M}|^2_{AB\to CD}+f_Cf_D|\mathcal{M}|^2_{CD\to AB}]$$ where $\mathcal{M}_{AB\to CD}$ and $\mathcal{M}_{CD\to AB}$ are the amplitudes of the forward and backward processes respectively, $H$ is the Hubble parameter. $d\pi_i$ and $f_i$ ($i=A,B,C,D$) are respectively the integrals over phase space and phase space distributions. Due to the $+$ sign on the RHS, the RHS is nonzero in chemical equilibrium even when $$\mathcal{M}_{AB\to CD}=\mathcal{M}_{CD\to AB},~\text{(assuming CP or T invariance)}$$ Therefore, $$\frac{dn}{dt}+3Hn\neq 0.$$ Therefore, the number density of species $A$ can change with time even when the dilution due to expansion is zero i.e., $H=0$. Therefore, the number density or the concentration of $A$ changes in even in chemical equilibrium.

Question Shouldn't the RHS of the Boltzmann equation be zero in chemical equilibrium in order to keep the concentration of each species unchanged with time?

Definition of chemical equilibrium According to the definition of chemical equilibrium in Wikipedia, it is a situation where the rate of the forward reaction is same as the rate of backward reaction and the concentrations of the reactants and the products do not change with time. I hope that the same definition applies to particle physics processes such as a 2-2 scattering of the form $A+B\leftrightarrow C+D$ i.e., in chemical equilibrium concentrations or number densities of each particle species remains unchanged with time.

Consistency of the definition with Boltzmann equation Boltzmann equation is used to study baryogenesis, relic abundance of dark matter and so on. According to Boltzmann equation, the number density $n$ of the species $A$ in an expanding Universe changes as: $$\frac{dn}{dt}+3Hn=\int d\pi_A d\pi_B d\pi_C d\pi_D[f_Af_B|\mathcal{M}|^2_{AB\to CD}+f_Cf_D|\mathcal{M}|^2_{CD\to AB}]$$ where $\mathcal{M}_{AB\to CD}$ and $\mathcal{M}_{CD\to AB}$ are the amplitudes of the forward and backward processes respectively, $H$ is the Hubble parameter. $d\pi_i$ and $f_i$ ($i=A,B,C,D$) are respectively the integrals over phase space and phase space distributions. Due to the $+$ sign on the RHS, the RHS is nonzero in chemical equilibrium even when $$\mathcal{M}_{AB\to CD}=\mathcal{M}_{CD\to AB},~\text{(assuming CP or T invariance)}$$ Therefore, $$\frac{dn}{dt}+3Hn\neq 0.$$ Therefore, the number density of species $A$ can change with time even when the dilution due to expansion is zero i.e., $H=0$. Therefore, the number density or the concentration of $A$ changes in even in chemical equilibrium.

Question Shouldn't the RHS of the Boltzmann equation be zero in chemical equilibrium in order to keep the concentration of each species unchanged with time?