Extremal principle of entropy production in the climate system

Abstract

SUMMARYPaltridge found reasonable values for the most significant climatic variables through maximizing the material transport part of entropy production by using a simple box model. Here, we analyse Paltridge's box model to obtain the energy and the entropy balance equations separately. Derived expressions for global entropy production, which is a function of the radiation field, and even its material transport component, are shown to be different from those used by Paltridge. Plausible climatic states are found at extrema of these parameters. Feasible results are also obtained by minimizing the radiation part of entropy production, in agreement with one of Planck's results. Finally, globally averaged values of the entropy flux of radiation and material entropy production are obtained for two dynamical extreme cases: an earth with uniform temperature, and an earth in radiative equilibrium at each latitudinal point.

Understanding Atmospheric Behaviour in Terms of Entropy: A Review of Applications of the Second Law of Thermodynamics to Meteorology

“…Without considering the detailed dynamics of the system, the predicted distributions (air temperature, cloud amount, and meridional heat transport) show remarkable agreement with observations [4]. Later on, several researchers investigated Paltridge's work and obtained essentially the same result [96][97][98][99][100][101][102][103]. Recently an information theoretical formulation of nonequilibrium statistical mechanics (MaxEnt, i.e., the constrained maximization of Shannon information entropy) is used to derive the fluctuation theorem (FT) concerning the probability of Second Law violating phase-space paths [104].…”

The second law of thermodynamics and the global climate system: A review of the maximum entropy production principle

“…Agreement of the two profiles is remarkable, despite the simple treatments used in his model. Later on, several researchers checked his work and obtained essentially the same results [e.g., Nicolis and Nicolis , 1980; Grassl , 1981; Mobbs , 1982; Noda and Tokioka , 1983; Sohn and Smith, 1993; O'Brien and Stephens , 1995; Ozawa and Ohmura , 1997; Pujol and Llebot , 1999a, 1999b, 2000a; Pujol and Fort , 2002; Pujol , 2003].…”

“…Without considering the detailed dynamics of the system, the predicted distributions (air temperature, cloud amount, and meridional heat transport) show remarkable agreement with observations. Later on, several researchers investigated Paltridge's work and obtained essentially the same result [ Grassl , 1981; Shutts , 1981; Mobbs , 1982; Noda and Tokioka , 1983; Sohn and Smith , 1993, 1994; Ozawa and Ohmura , 1997; Pujol and Llebot , 1999a, 1999b]. His suggestion was criticized by Essex [1984], however, since a predominant amount of entropy production is due to direct absorption of solar radiation at the Earth's surface, which was a missing factor in Paltridge's work.…”

Greenhouse gases and climatic states of minimum entropy production

“…Moreover, comparison of the values obtained for both $,• and •.., to those for •t and fro, corresponding to the present state, indicate that the current climate does not follow maximum behavior, neither in total nor in matter entropy production within North's [1975a, b] 1-D model. However, the climate seems to tend to a given state where the extreme of the difference between ftm and from (•'m, say) equals the value for the radiative entropy production •.. We shall here refer to •rn as the minimum radiative entropy production, following ?ujol and Llebot [1999a], who found that the state of miniinure radiative entropy production in Paltridge's 1-D box model is nearly equivalent to the states that satisfy both ftm or from conditions. (10)).…”