Can thermodynamic equilibrium be established in planet-forming disks?

The inner regions of planet-forming disks are warm and dense. The chemical networks used for disk modelling so far were developed for a cold and dilute medium and do not include a complete set of pressure-dependent reactions. The chemical networks developed for planetary atmospheres include such reactions along with the inverse reactions related to the Gibb's free energies of the molecules. The chemical networks used for disk modelling are thus incomplete in this respect. We want to study whether thermodynamic equilibrium can be established in a planet-forming disk. We identify the regions in the disk most likely to reach thermodynamic equilibrium and determine the timescale over which this occurs. We employ the theoretical concepts used in exoplanet atmosphere chemistry for the disk modelling with PROtoplanetary DIsk MOdel ({\sc ProDiMo}). We develop a chemical network called CHemistry Assembled from exoplanets and dIsks for Thermodynamic EquilibriA ({\sc ChaiTea}) that is based on the UMIST 2022, STAND, and large DIscANAlysis (DIANA) chemical networks. It consists of 239 species. From the STAND network, we adopt the concept of reversing all gas-phase reactions based on thermodynamic data. We use single-point models for a range of gas densities and gas temperatures to verify that the implemented concepts work and thermodynamic equilibrium is achieved in the absence of cosmic rays and photoreactions including radiative associations and direct recombinations. We then study the impact of photoreactions and cosmic rays that lead to deviations from thermodynamic equilibrium. We explore the chemical relaxation timescales towards thermodynamic equilibrium. Lastly, we study the predicted 2D chemical structure of a typical T\,Tauri disk when using the new {\sc ChaiTea} network instead of the large DIANA standard network, including photorates, cosmic rays, X-rays, and ice....