Exoplanet direct imaging is a rapidly progressing area of study and a key driver of proposed space-based mission concepts, such as HabEx and LUVOIR. This search for life on directly imaged worlds will depend on our ability to remotely detect atmospheric tracers for life (i.e., biosignatures). In this work, we focus on the detectability of chemical disequilibrium biosignatures. We adopt the available Gibbs free energy as a metric to quantify chemical disequilibrium for an atmospheric system. Critically, the Gibbs free energy can be rapidly calculated using thermodynamic modeling tools. Using retrieval techniques and a Bayesian Markov chain Monte Carlo tool, we retrieve key atmospheric parameters from simulated spectroscopic observations of an Earth-like exoplanet. We couple our statistical constraints on atmospheric state parameters to a thermodynamic Gibbs free energy model to understand potential constraints on chemical disequilibrium. Additionally, we explore the sensitivity to planetary properties that are unlikely to be constrained via spectroscopic observations (e.g., ocean volume). Through this process, we assess the remote detectability of the Gibbs free energy for an Earth-like exoplanet atmosphere-ocean system.