  Atmospheric chemical disequilibrium has been proposed as a method for
detecting extraterrestrial biospheres from exoplanet observations. Chemical
disequilibrium is potentially a generalized biosignature since it makes no
assumptions about particular biogenic gases or metabolisms. Here, we present
the first rigorous calculations of the thermodynamic chemical disequilibrium in
Solar System atmospheres, in which we quantify the available Gibbs energy: the
Gibbs free energy of an observed atmosphere minus that of atmospheric gases
reacted to equilibrium. The purely gas phase disequilibrium in Earth's
atmosphere is mostly attributable to O2 and CH4. The available Gibbs energy is
not unusual compared to other Solar System atmospheres and smaller than that of
Mars. However, Earth's fluid envelope contains an ocean, allowing gases to
react with water and requiring a multiphase calculation with aqueous species.
The disequilibrium in Earth's atmosphere-ocean system (in joules per mole of
atmosphere) ranges from 20 to 2E6 times larger than the disequilibria of other
atmospheres in the Solar System. Only on Earth is the chemical disequilibrium
energy comparable to the thermal energy per mole of atmosphere. Earth's
disequilibrium is biogenic, mainly caused by the coexistence of N2, O2 and
liquid water instead of more stable nitrate. In comparison, the O2-CH4
disequilibrium is minor. We identify abiotic processes that cause
disequilibrium in the other atmospheres. Our metric requires minimal
assumptions and could potentially be calculated using observations of exoplanet
atmospheres. However, further work is needed to establish whether thermodynamic
disequilibrium is a practical exoplanet biosignature, requiring an assessment
of false positives, noisy observations, and other detection challenges. Our
Matlab code and databases for these calculations are available, open source.
