## 1. Introduction

Atmospheric and climate dynamics rank among the most complex phenomena encountered in nature. They involve processes occurring over a wide spectrum of space- and time-scales, from the chemistry of minor constituents in the stratosphere to hurricanes, droughts or the Quaternary glaciations, and give rise to a variety of intricate behaviours in the form of abrupt transitions, wave propagation, weak chaos or fully developed turbulence.

The generally accepted approach to atmospheric and climate dynamics is based on numerical forecasting models, in which all processes deemed to be relevant are included in the model equations. This introduces a large number of variables and heavy parametrizations, often at the expense of a deeper understanding of the principal mechanisms behind the phenomenon of interest. It is therefore tempting to seek the possibility of universal trends in the form of ‘organizing principles’ underlying key aspects of atmospheric and climate dynamics, which could end up being masked in the context of a full-scale analysis.

An elegant and far-reaching expression of universality is the formulation of *variational principles*. The idea is that, whatever the specifics might be, among all possible paths that may link an initial state to a final one, the path that will actually be followed under the action of the evolution laws of the system of interest extremizes a certain quantity. In classical physics and at the microscopic level of description in which the system's state variables are the positions and momenta of the constituting particles, a celebrated variational principle of this sort is the principle of least action (Arnold, 1976). The extent to which results of this kind can also be expected at the macroscopic level of description as well, in which the laws governing atmospheric and climate dynamics are usually formulated, has attracted a great deal of interest over the last several decades. Research in irreversible thermodynamics and nonlinear dynamics has shown that variational properties involving only macroscopic variables may exist under some well-defined (and rather stringent) conditions such as the linear range of irreversible processes (minimum entropy production theorem) or the vicinity of a bifurcation at a simple real eigenvalue (in which case the dynamics derives from a generalized, *kinetic* potential). In contrast, in the most general case of systems operating far from criticalities and far from the state of thermodynamic equilibrium, there exists no variational principle generating the full form of the evolution equations (Glansdorff and Prigogine, 1971; Nicolis and Nicolis, 2007).

Despite this negative conclusion, a number of approaches based on the existence of an extremum principle have been reported in the atmospheric and climate literature. Most familiar is the one originally proposed by Paltridge (1975, 1981) that global climate is a state of maximum dissipation. The idea has been taken up by several authors, both in the atmospheric and climatic (Ozawa *et al.*, 2003, and references therein) and the general physics (Martyushev and Seleznev, 2006, and references therein) literatures and, eventually, the concept of ‘maximum entropy production principle’ has emerged. As the very term ‘principle’ implies, support of this statement came mainly from circumstantial evidence or from qualitative arguments and there is currently no direct proof available, as a recent attempt to that effect (Dewar, 2005) was subsequently shown to be unfounded (Grinstein and Linsker, 2007). In the present work, the maximum entropy production principle is reassessed. We show that the tendency to maximize dissipation does not reflect a universal trend but is, rather, system specific. Put differently, a general thermodynamic principle underlying the evolution of complex nonlinear systems out of equilibrium and based on the properties of the entropy production—the basic thermodynamic quantity measuring dissipation—is not to be expected, at least as long as a macroscopic description is adopted. Our approach is dynamics-driven, in the sense that we inquire whether the laws governing the evolution of a natural phenomenon may lead to extremal properties reminiscent of maximum dissipation. This is to be contrasted with a number of other approaches (e.g. Dewar, 2005) where extremal principles are postulated at the outset on the basis of information theoretic arguments.

In what follows we focus, successively, on three key points that have been advanced to support the idea of a maximum dissipation principle. In section 2 the hypothesis that a nonlinear system will move, when perturbed, to a ‘dominant’ state in which entropy production is a maximum is addressed, and a number of counterexamples are provided. In section 3 the idea that the deterministic trajectory, which constitutes the most probable state of a system subjected to fluctuations, dissipates more than any of its fluctuating counterparts is considered. An extension of classical irreversible thermodynamics incorporating the effect of fluctuations is outlined. A generalized expression of the associated entropy production is derived, from which is concluded that fluctuations may, in the mean, enhance or depress the dissipation compared with the dissipation on the most probable state. Section 4 is devoted to a reformulation of the proposal of global climate as a system of maximum dissipation, in the light of the analysis of section 3. Again, no basis in favour of such a property is found. The main conclusions are summarized in section 5.