  We study the thermodynamic efficiency of the Malkus-Lorenz waterwheel. For
this purpose, we derive an exact analytical formula that describes the
efficiency of this dissipative structure as a function of the phase space
variables and the constant parameters of the dynamical system. We show that,
generally, as the machine is progressively driven far from thermodynamic
equilibrium by increasing its uptake of matter from the environment, it also
tends to increase its efficiency. However, sudden drops in the efficiency are
found at critical bifurcation points leading to chaotic dynamics. We relate
these discontinuous crises in the efficiency to a reduction of the attractor's
average value projected along the phase space dimensions that contribute to the
rate of entropy generation in the system. In this manner, we provide a
thermodynamic criterion that, presumably, governs the evolution of
far-from-equilibrium dissipative systems towards their self-assembly and
synchronization into increasingly complex networks and structures.

Statistical Mechanics;Chaotic Dynamics