  We show that active transport processes in biological systems can be
understood through a local equilibrium description formulated at the mesoscale,
the scale to describe stochastic processes. This new approach uses the method
established by nonequilibrium thermodynamics to account for the irreversible
processes occurring at this scale and provides nonlinear kinetic equations for
the rates in terms of the driving forces. The results show that the application
domain of nonequilibrium thermodynamics method to biological systems goes
beyond the linear domain. A model for transport of Ca$^{2+}$ by the
Ca$^{2+}$-ATPase, coupled to the hydrolysis of adenosine-triphosphate is
analyzed in detail showing that it depends on the reaction Gibbs energy in a
non-linear way. Our results unify thermodynamic and kinetic descriptions,
thereby opening new perspectives in the study of different transport phenomena
in biological systems.
