There is an interesting to and fro over at Real Climate about the recent Hansen, Ruedy and Sato paper on an increase in climate extremes. Eli had a go at the preprint. Tamino has entered a demurral, which Eli suspects has an answer in what is below. Now some, not Eli to be sure, think the Rabett is on occasion cryptic. So be it, but in this case he has not quite worked through all the implications and it is better to be thought mysterious than foolish. Still the Bunny is somewhat skilled in boiling things down, and at RC pointed out that there are three simple points in the Hansen paper
First if there is an increasing/decreasing linear trend on a noisy series, the probability of reaching new maxima or minima increases with timeHank added a codicil
Second, if you put more energy into a system variability increases.
Third, if you put more energy into a system variability increases asymmetrically towards the direction favored by higher energy
Fourth, if you keep going in the direction you’re headed, you’ll get there.The first point has been a standard here at RR and also in various comments about the web in the recent discussions about why there are more temperature maxima than minima. The second is related to the idea that if the parametric landscape affecting anything is not smooth, excursions from a stable state require additional energy to overcome "attractions".
For example, if you are in a low energy valley, as you add energy, the system moves higher up the sides and the range of motion becomes larger. As examples consider potential energy surfaces for any process such as chemical reactions, protein unfolding, etc. The third comes from the same general area, that if there are barriers to some excursions, you enhance the probability of exceeding them only with additional energy, e.g. you have to climb the mountain to get to the next valley, Hank's Law.
UPDATE: Perhaps a hint of where the second and third law come from in answer to some questions
taken from protein folding paper. The same arguments cover many situations including climate. If we start at the bottom of the U(nfolded) well with only a small amount of energy available, the motion is roughly harmonic. This is a logical consequence of the stability, because the point at the bottom of the well is where the system would come to rest if energy were zero and the first term in the Taylor series expansion of the potential would be quadratic Small additional amounts of energy result in harmonic (symmetric) motion in first approximation (brown and red line.
As more energy is added you get pushed to the level of the green line, where there is more variation in the reaction coordinate as in the second law. Finally if you reach the level of the red line, further areas of the parameter space become available and you can access the folded form. The ability to access new areas of the potential is what drives the asymmetry.