Why could oxygen or methane in an exoplanet atmosphere be possible evidence of life?

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In the field of astrobiology, the detection of oxygen or methane in an exoplanet's atmosphere is considered potential evidence of life because these gases often indicate a state of thermodynamic disequilibrium.1

On Earth, the atmosphere contains large amounts of molecular oxygen and methane that would not coexist in such high concentrations if the planet were lifeless. In thermodynamic equilibrium, methane should be present in only negligible amounts because it is highly reactive and would be oxidized. The fact that it remains at a steady-state abundance implies a continuous, rapid source of production. While non-biological processes can sometimes produce these gases, a biological explanation is often more likely, as these compounds are key by-products of metabolic processes like photosynthesis and the activity of methanogenic bacteria.1234

Consequently, remote-sensing methods seek such chemical disequilibria as a "preliminary positive test" for life. However, scientists must be cautious, as these signatures can be ambiguous; for instance, oxygen can also be produced by the photodissociation of water vapor.12