Free energy and dissipation rate for reaction diffusion processes of electrically charged species

The paper deals with a special problem concerning the transport of electrically charged species via diffusion, drift, and reaction mechanisms. We prove for a variety of models that without knowing any a priori estimate for the chemical potentials one can estimate the free energy from above by the corresponding dissipation rate. The inequality presented here can be interpreted as a nonlinear analogue of Korn's Inequality or PoincarC's Inequality. As a consequence of our main result we show that the free energy approximates its equilibrium value exponentially as time tends to infinity.