Extremal principle of entropy production in the climate system

Paltridge 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

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

The long-term mean properties of the global climate system and those of turbulent fluid systems are reviewed from a thermodynamic viewpoint. Two general expressions are derived for a rate of entropy production due to thermal and viscous dissipation (turbulent dissipation) in a fluid system. It is shown with these expressions that maximum entropy production in the Earth s climate system suggested by Paltridge, as well as maximum transport properties of heat or momentum in a turbulent system suggested by Malkus and Busse, correspond to a state in which the rate of entropy production due to the turbulent dissipation is at a maximum. Entropy production due to absorption of solar radiation in the climate system is found to be irrelevant to the maximized properties associated with turbulence. The hypothesis of maximum entropy production also seems to be applicable to the planetary atmospheres of Mars and Titan and perhaps to mantle convection. Lorenz s conjecture on maximum generation of available potential energy is shown to be akin to this hypothesis with a few minor approximations. A possible mechanism by which turbulent fluid systems adjust themselves to the states of maximum entropy production is presented as a selffeedback mechanism for the generation of available potential energy. These results tend to support the hypothesis of maximum entropy production that underlies a wide variety of nonlinear fluid systems, including our planet as well as other planets and stars

Public and Private Production in a Mixed Delivery System: Regulation, Competition and Costs

Academics and policy makers are increasingly shifting the debate concerning the best form of public service provision beyond the traditional dilemma between pure public and pure private delivery modes, because, among other reasons, there is a growing body of evidence that casts doubt on the existence of systematic cost savings from privatization, while any competition seems to be eroded over time. In this paper we compare the relative merits of public and private delivery within a mixed delivery system. We study the role played by ownership, transaction costs, and competition on local public service delivery within the same jurisdiction. Using a stochastic cost frontier, we analyze the public-private urban bus system in the Barcelona Metropolitan Area. Our results suggest that private firms tendering the service have higher delivery costs than those incurred by the public firm, especially when transaction costs are taken into account. Tenders, therefore, do not help to reduce delivery costs. Our results suggest that under a mixed delivery scheme, which permits the co-existence of public and private production, the metropolitan government and the regulator can use private delivery to contain costs in the public firm and, at the same time, benefit from the greater flexibility of private firms for dealing with events not provided for under contract.