Equilibrium meander bends shift downstream with a constant speed while maintaining a coherent form. Based on a dynamical description of flow in alluvial river bends and a kinematic description of continuous bank erosion, Parker et al. (1983) derived a class of equilibrium meander planform shapes known as Kinoshita curves. These equilibria were found to be unstable, which has lead to the common idealized view that meanders alternately elongate by gradual bend erosion and shorten due to cut-off, and do not reach a true equilibrium. It is herein argued that the extremely slow rate of change of near-equilibrium meanders in conjunction with neglected aspects such as time variation of the threshold of sediment motion can be the reason why most undisturbed meanders found in nature are in fact near-equilibrium. It is therefore worthwhile to further examine and describe equilibrium meanders, which is the subject of the present study. Starting from the hypothesis that for equilibrium meanders the variance of entropy production is minimized, most probable planform parameter values are derived that determine how fattening and skewing (parameterized by cf and cs, respectively) of an equilibrium meander depend on sinuosity. Sinuosity, in turn, is mainly externally controlled. It is shown how the hypothesis ofminimumvariance of entropy production practically boils down to the assumption ofminimization of channel morphology change rates, revealing the mechanistic interpretation of the theory. The validity of our hypothesis is elucidated by a comparison with twenty four meander reaches of various geographical locations, and by the fact that for arbitrary sinuosities a unique minimum for the variance of entropy production in the (cf, cs)-plane exists.