## Does a global temperature exist?(English)Zbl 1130.80004

The authors of this article, who are experts in non-equilibrium thermodynamics, point out obvious weaknesses of any effort attempting to define statistically “global temperature”, and consequently they ask the crucial question “can global temperature be defined?”
The geographers, and Space Institutes (Goddard Institute for example) do not seem to have such serious problems. They measured and averaged daily temperatures in various regions scattered around the Earth, such as the Arctic Ocean and Antarctica, and in several points around the globe, they looked at the area covered by ice in the Arctic, at depth of the ice in Antarctica, and came to a simple decision, that on the whole the earth is getting warmer. Then they produced the concept of annual global temperature for the Earth. They claimed accuracy of $$\pm 0.05$$.
The authors of the article under review reply to such naive approach in a manner similar to C. Truesdell ’s attack on traditional thermodynamics [The tragicomical history of thermodynamics 1822–1854. New York etc.: Springer (1980; Zbl 0439.01012)], claiming that the notation and some mathematical definitions of the concepts of classical thermodynamics left much to be desired. In particular the authors insist that the annual global temperature is a poorly defined concept, for a system far from equilibrium. In fact, in such system temperature cannot be defined by simply averaging samplings made at discrete time intervals. The reviewer comments that dimensional analysis would also easily confirm the authors’ objections to existence of global annual temperature. To argue this point we recognize existence of extensive and intensive variables. Extensive variables are additive. They include mass $$m$$, energy $$U$$, entropy $$S$$. As we combine many systems, the total mass shall be equal to the sum of the masses, etc.…This sum is divided by the number of component masses. Such operation of finding the average is meaningful. Summing intensive variables, such as pressure or temperature, and then averaging by division of number of components, has no physical meaning. The equation $$T= \partial U/\partial S$$, defining the temperature has many legitimate, and more complex, statistical averaging processes, which are discussed by the authors. The authors also go into details of what is wrong with a single real number $$\Xi$$, used as a statistical measure of “anomaly”, i.e. of global warming.
The authors do not argue against measurements of the area covered by ice in the Arctic Ocean, or other observed instances indicating climatic changes. They only object to the “theoretical” approaches consisting of the simplest possible, and incorrect, averaging of such phenomena. The reviewer found this article timely and very interesting.

### MSC:

 80A05 Foundations of thermodynamics and heat transfer 82C35 Irreversible thermodynamics, including Onsager-Machlup theory 86A10 Meteorology and atmospheric physics 86A05 Hydrology, hydrography, oceanography

Zbl 0439.01012
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### References:

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