  A huge amount of entropy is produced at places where fresh water and seawater
mix, for example at river mouths. This mixing process is a potentially enormous
source of sustainable energy, provided it is harnessed properly, for instance
by a cyclic charging and discharging process of porous electrodes immersed in
salt and fresh water, respectively [D. Brogioli, Phys. Rev. Lett. 103, 058501
(2009)]. Here we employ a modified Poisson-Boltzmann free-energy density
functional to calculate the ionic adsorption and desorption onto and from the
charged electrodes, from which the electric work of a cycle is deduced. We
propose optimal (most efficient) cycles for two given salt baths involving two
canonical and two grand-canonical (dis)charging paths, in analogy to the
well-known Carnot cycle for heat-to-work conversion from two heat baths
involving two isothermal and two adiabatic paths. We also suggest a slightly
modified cycle which can be applied in cases that the stream of fresh water is
limited.
