  Chemical disequilibrium quantified via available free energy has previously
been proposed as a potential biosignature. However, exoplanet biosignature
remote sensing work has not yet investigated how observational uncertainties
impact the ability to infer a life-generated available free energy. We pair an
atmospheric retrieval tool to a thermodynamics model to assess the
detectability of chemical disequilibrium signatures of Earth-like exoplanets,
emphasizing the Proterozoic Eon where atmospheric abundances of oxygen-methane
disequilibrium pairs may have been relatively high. Retrieval model studies
applied across a range of gas abundances revealed that order-of-magnitude
constraints on disequilibrium energy are achieved with simulated
reflected-light observations at the high abundance scenario and signal-to-noise
ratios (50) while weak constraints are found at moderate SNRs (20\,--\,30) for
med\,--\,low abundance cases. Furthermore, the disequilibrium energy
constraints are improved by modest thermal information encoded in water vapor
opacities at optical and near-infrared wavelengths. These results highlight how
remotely detecting chemical disequilibrium biosignatures can be a useful and
metabolism-agnostic approach to biosignature detection.
