  Classical theories of chemical kinetics assume independent reactions in
dilute solutions, whose rates are determined by mean concentrations. In
condensed matter, strong interactions alter chemical activities and create
inhomogeneities that can dramatically affect the reaction rate. The extreme
case is that of a reaction coupled to a phase transformation, whose kinetics
must depend on the order parameter -- and its gradients, at phase boundaries.
This Account presents a general theory of chemical kinetics based on
nonequilibrium thermodynamics. The reaction rate is a nonlinear function of the
thermodynamic driving force (free energy of reaction) expressed in terms of
variational chemical potentials. The Cahn-Hilliard and Allen-Cahn equations are
unified and extended via a master equation for non-equilibrium chemical
thermodynamics. For electrochemistry, both Marcus and Butler-Volmer kinetics
are generalized for concentrated solutions and ionic solids. The theory is
applied to intercalation dynamics in the phase separating Li-ion battery
material Li$_x$FePO$_4$.
