Entropy production and dynamical complexity in a low‐order atmospheric model

Lorenz's classical model of thermal convection is analysed from the standpoint of irreversible thermodynamics. the entropy production, describing how dissipative processes are operating within the system, is expressed in terms of the model variables. It is subsequently evaluated in different parts of the attractor and the values so obtained are compared with various indicators of the complexity of the dynamics, such as the local Lyapunov exponents and a local generalization of the Kolmogorov entropy. As it turns out, dissipative processes are most efficient when the number of locally stable directions increases. In particular, when the local Kolmogorov entropy is close to zero (three stable directions) the system can dissipate over the entire spectrum of values available. Finally, it is shown that the evolution on the attractor does not correspond to any extremal property of the entropy production.