Plain-language summary. The climate has large-scale flows: the winds that move heat from the equator toward the poles, the slow overturning of the oceans, and the jet streams that steer our weather. Under one and the same set of conditions, these flows can sometimes settle into more than one stable pattern, much as a ball can come to rest in any of several valleys in a hilly landscape. A well-known idea, maximum entropy production (MEP), says that the pattern nature actually picks is the one that uses up energy the fastest. This paper does not set out to confirm or reject that idea, but to pin down when it holds. The key turns out to be which pattern is most stable: the one that random disturbances find hardest to push the system out of, like the deepest valley in a hilly landscape (physicists measure this by a quantity called the quasi-potential). How fast a pattern dissipates energy is one part of what makes it stable, but only one part. The rest depends on how vigorously the small-scale, turbulent motions churn (a quantity called frenesy), which climate models cannot work out directly and instead put in by hand, through simplified recipes for the turbulence. Change the recipe and you can change which pattern wins. So MEP gives the right answer when fast dissipation lines up with deep stability, and it can mislead when it does not; telling the two cases apart is what the paper aims to make possible. The paper shows this with a few small models that can be worked out in full, including a standard model of a real atmospheric flow: equatorial superrotation, where the high-altitude winds race eastward faster than the planet turns. When the turbulence enters through a single channel, the fast-dissipating pattern wins, just as MEP expects. When it enters through two channels, the slower-dissipating pattern can win instead. This happens only in a minority of cases, and it is always the deeper valley that wins. The paper also gives a quick shortcut that uses only the steady states themselves: in the range tested it correctly predicts which cases will flip about nine times out of ten, and it never errs in the risky direction. Why it matters. Researchers across Earth science use MEP as a quick way to guess which large-scale state a model, or the real climate, will end up in: heat transport in the atmosphere, ocean circulation, and the switch between a frozen "snowball" Earth and an ice-free one. If MEP were a dependable law, it would be a simple and very general way to make these guesses. This paper shows that MEP is better seen not as a universal law but as a conditional one: it holds when the model's turbulence recipe keeps the extra churning effect small, and it can fail when that effect is large. What the paper offers instead is a checklist of the conditions that must hold before an MEP guess can be trusted, together with the quick shortcut above for spotting when a particular turbulence recipe is likely to overturn the guess. So MEP is better treated as a case-by-case diagnostic to be checked, not a universal law, and the checklist shows where it can go wrong. This is a conceptual and methodological result; it does not by itself yield new quantitative predictions about the real climate. But the caution it raises is general: it applies whenever some change in the climate's drivers (a shift in sunlight, in aerosols, in greenhouse gases, or anything else) could move the system from one large-scale pattern to another, and in any such case it tells you when entropy-based reasoning about which pattern is chosen can be trusted, and when it cannot.
Shigeo Kaneko (Wed,) studied this question.