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The atmospheric carbon-to-oxygen ratio compares the elemental abundances of carbon and oxygen in the atmosphere. It influences molecular composition under chemical equilibrium, but condensation, disequilibrium chemistry in an exoplanet atmosphere, and incomplete spectral coverage complicate its inference from molecular bands.

Condensation followed by gravitational settling removes chemical elements from an atmospheric layer. The remaining gas may be in local chemical equilibrium with a depleted elemental inventory, while the column is not a closed equilibrium system.

A massive decoupled sector enters a cannibal phase when its particles are nonrelativistic but rapid number-changing reactions maintain chemical equilibrium and zero chemical potential from number-changing reactions. Rest-mass energy released by $3\to 2$ reactions heats the remaining particles, so the sector cools much more slowly than an isolated number-conserving nonrelativistic gas. The temperature laws follow directly from cosmological entropy conservation. An example is discussed in Cannibal Dark Matter.

A chemical system is out of local chemical equilibrium when reaction adjustment cannot keep pace with transport, imposed changes or external driving. Comparing the chemical relaxation time with transport and irradiation times identifies plausible departures. Disequilibrium chemistry in an exoplanet atmosphere combines this principle with mixing, horizontal advection and atmospheric photochemistry.

The chemical relaxation time estimates how rapidly a perturbed abundance returns toward chemical equilibrium. Comparing it with the eddy mixing time identifies a chemical quench level.

For chemical equilibrium $D\leftrightarrow n+p$, Maxwell--Boltzmann densities and ${\mu }_D={\mu }_n+{\mu }_p$ give, after taking $m_n\simeq m_p$ and $m_D\simeq 2m_p$,Writing $X_i=n_i/n_B$, $n_B=\eta n_{\gamma }$, and $n_{\gamma }=16\pi \zeta (3)(k_{B}T{)}^3/(hc{)}^3$ givesThe very small baryon-to-photon ratio suppresses deuterium until $T$ is far below the binding-energy scale.

Thermal electron-positron pairs in chemical equilibrium with photons have opposite chemical potentials when the one-particle energy includes rest energy. For negligible degeneracy and $k_{B}T\ll m_e{c}^2$, the zero-chemical-potential density per charge species is $n_0=2[m_e{k}_{B}T/(2\pi {\hslash }^2){]}^{3/2}{e}^{-m_e{c}^2/(k_{B}T)}$. In that nondegenerate limit, charge neutrality and the classical equilibrium product $n_{-}{n}_{+}=n_0^2$ give $n_{+}=(\sqrt{n_b^2+4n_0^2}-n_b)/2$, with net Electron density $n_b$. Pairs are important when $n_0\gtrsim n_b$. At arbitrary temperature the zero-chemical-potential marker uses the integral $n_0=({\pi }^2{\hslash }^3{)}^{-1}{\int }_0^{\infty }{p}^2[\exp (\sqrt{m_e^2{c}^4+p^2{c}^2}/k_{B}T)+1{]}^{-1}dp$. Its ultrarelativistic limit is $3\zeta (3)(k_{B}T/\hslash c{)}^3/(2{\pi }^2)$. A nonzero net chemical potential shifts the exact abundance boundary; the zero-potential curve is an approximate crossover marker.

Momentum-exchange collisions maintain a common temperature and an equilibrium-shaped momentum probability distribution. Particle abundances and chemical potentials need not have their chemical equilibrium values: elastic scattering alone conserves particle number. Thus kinetic equilibrium does not by itself imply either zero chemical potential or conserved comoving entropy.