  The Lorenz system was derived on the basis of a model of convective
atmospheric motions and may serve as a paradigmatic model for considering a
complex climate system. In this study, we formulated the thermodynamic
efficiency of convective atmospheric motions governed by the Lorenz system by
treating it as a non-equilibrium thermodynamic system. Based on the fluid
conservation equations under the Oberbeck-Boussinesq approximation,the work
necessary to maintain atmospheric motion and heat fluxes at the boundaries were
calculated. Using these calculations, the thermodynamic efficiency was
formulated for stationary and chaotic dynamics. The numerical results show
that, for both stationary and chaotic dynamics, the efficiency tends to
increase as the atmospheric motion is driven out of thermodynamic equilibrium
when the Rayleigh number increases. However, it is shown that the efficiency is
upper bounded by the maximum efficiency, which is expressed in terms of the
parameters characterizing the fluid and the convective system. The analysis of
the entropy generation rate was also performed for elucidating the difference
between the thermodynamic efficiency of conventional heat engines and the
present atmospheric heat engine. It is also found that there exists an abrupt
drop in efficiency at the critical Hopf bifurcation point, where the dynamics
change from stationary to chaotic. These properties are similar to those found
previously in Malkus-Lorenz waterwheel system.
