Eyring equation and fluctuation-dissipation far away from equilibrium

Understanding and managing the influence that either external forces or non-equilibrated environments may have on chemical processes is essential for the current and future development of theoretical chemistry. One of the central questions to solve is how to generalize the transition state theory in order to make it applicable in far from equilibrium situations. In this sense, here we propose a way to generalize Eyring's equation based on the definition of an effective thermal energy (temperature) emerging from the coupling of both fast and slow dynamic variables analyzed within the generalized Langevin dynamics scheme. This coupling makes the energy distribution of the fast degrees of freedom not equilibrate because they have been enslaved to the dynamics of the corresponding slow degrees. However, the introduction of the effective thermal energy enables us to restore an effective adiabatic separation of timescales leading to a renormalization of the generalized fluctuation-dissipation theorem. Hence, this procedure opens the possibility to deal with systems far away from equilibrium. A significant consequence of our results is that Eyring's equation is generalized to treat systems under the influence of strong external forces.