The physicist’s free energy, read through the information-geometric lens, is the log-partition of a Gibbs family. It is a state function whose differences carry the physics whereas its absolute value does not, which is why binding affinities live in a cycle of ‘s.
For a system with states , energy , and inverse temperature , the (Helmholtz) free energy is with partition function . It scores the trade-off between energy and entropy, , and coincides with the log-partition up to the factor . The Gibbs free energy adds a term for constant-pressure systems. Free energy is a state function, so only differences between states are physical, and around any closed cycle they sum to zero. This additivity is what alchemical thermodynamic networks exploit. A binding affinity is one such difference, , obtained as a path or cycle of estimates.
References
S. Amari, Information Geometry and Its Applications (2016)