Earth's Entropy

Abstract

Ralph Lorenz's Perspective “Full steam ahead—probably” (7 Feb. 2003, p. [837][1]) on the recent groundbreaking work of Roderick Dewar ([1][2]) mentions the puzzle that “All else being equal, MEP [maximum entropy production] would predict a planet's meridional temperature contrast to be independent of its rotation rate. This disagrees with some rudimentary GCM [general circulation model] experiments, and with meteorologists' intuition.” It is well known that tidal and atmospheric motions exert torque on the solid Earth, which detectably affects its rotation rate ([2][3], [3][4]). Hadley-cell-driven trade winds, for example, exert torque on Earth's surface in a direction that promotes continued rotation. This could conceivably amount to ordered work that acts as an additional mode of entropy production. Perhaps climate modelers should investigate whether one consequence of maximum entropy production on Earth may be partial regulation of planetary rotation rate. 1. 1.[↵][5]1. R. L. Dewar , J. Phys. A. Math. Gen. 36, 631 (2003). [OpenUrl][6][CrossRef][7] 2. 2.[↵][8]See . 3. 3.[↵][9]See . # Response {#article-title-2} Phillips suggests that thermodynamics may guide planetary rotations. For Earth, at least, this is unlikely to be so. The usefulness of maximum entropy production (MEP) is only as a selection guideline among dynamically permitted steady states, and the rotation state of the planet may control which states are dynamically possible. The system must first comply with the rigid laws of physics, notably the conservation of mass, energy, and angular momentum: These factors are imposed as constraints on the system before MEP applies. Even if Earth's whole atmosphere were to spin up to the speed of sound (an extreme case!), angular momentum balance means the rotation period of the solid Earth (where much of the solar heat is absorbed and reradiated) changes by only about one part in one million—a level unlikely to affect heat transfer. Thus, even if the dynamics allowed such a spin-up, it seems the system would gain little from the effort. However, Phillips' basic suggestion, that optimality in heat transport may guide rotation rates, may have merit for the atmospheres of extrasolar giant planets ([1][10]) where atmospheric motions at the relatively high altitudes where starlight is absorbed and thermal radiation emitted are largely decoupled from the motion of the planet's interior. If the motions are guided by an MEP heat transport criterion, close-in extrasolar planets, even if tidally locked to their parent star, may nonetheless have only modest day: night temperature contrasts. 1. 1.[↵][11]1. J. I. Lunine, 2. R. D. Lorenz , “A simple prescription for calculating day-night temperature contrasts on synchronously rotating planets,” 33rd Annual Lunar and Planetary Science Conference, 11 to 15 March 2002, Houston, TX, abstr. no. 1429. [1]: /lookup/doi/10.1126/science.1081280 [2]: #ref-1 [3]: #ref-2 [4]: #ref-3 [5]: #xref-ref-1-1 View reference 1. in text [6]: {openurl}?query=rft.jtitle%253DJ.%2BPhys.%2BA.%2BMath.%2BGen.%26rft.volume%253D36%26rft.spage%253D631%26rft_id%253Dinfo%253Adoi%252F10.1088%252F0305-4470%252F36%252F3%252F303%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [7]: /lookup/external-ref?access_num=10.1088/0305-4470/36/3/303&link_type=DOI [8]: #xref-ref-2-1 View reference 2. in text [9]: #xref-ref-3-1 View reference 3. in text [10]: #ref-4 [11]: #xref-ref-4-1 View reference 1. in text