Transition state theory in systems of interacting particles

Chemical equilibrium is fully characterized at thermodynamic level by the free energy: the equilibrium is written in terms of equality of chemical potentials. Rate of chemical reactions can be calculated for ideal solutions by using mass-action equations, with reaction rate constants related to energy barriers through the transition state theory. The two approaches merge in the case of equilibrium and ideal solutions. Here, we discuss how to extend the transition state theory in the case of non-ideal solutions, i.e. of interacting particles, at equilibrium. We find bounds of the exchange reaction rate. However, we show that the value of the exchange reaction rate cannot be calculated from equilibrium thermodynamic parameters (i.e. from the free energy), i.e. it is possible to find different Hamiltonians giving the same free energy but different exchange reaction rate.