Just as a reminder what a couple of those words mean:
Kurtosis is the tendency for something to be a non-Gaussian distribution. Things where the sides of the curve are ‘fatter’ than usual; or similar non-random distributions. Think of a “bell curve” that has fatter ends with many more outlier data points.
Mpemba is the name stuck on the observation that sometimes warm water freezes faster than cold water. It is the name of a kid Tanzania who observed that he got ice cream faster if he used warm milk.
Kurtosis is important in the real world; but both things are widely ignored and misunderstood.
Substantially every intro stats class has a part where they stress that what they are teaching you applies only to a Gaussian distribution. (Later advanced stats relaxes that with other distributions). Most folks with only an intro to statistics rapidly forget that and try to apply those tools to all sorts of things without bothering to examine the distribution of their data first. That’s a fundamental error, and it is rampant in “Climate Science”.
Pretty much all we are taught about freezing water presumes a known standard heat of fusion, heat of vaporization, and specific heat. But the Mpemba Effect demonstrates that is not quite right. This assumption of known heats is also rampant in “Climate Science”, but it is not clear if it maters (where the statistics errors are known to be a big deal).
So instead of just poo-pooing the folks saying hot water freezes faster, some smart guys decided to actually investigate it. Water, being rather complex to study, they hit on the bright idea of studying a simpler material. They used a “granular gas”. What the heck is that? Well, turns out you can study things like sand as though it were a gas…
Now mix those three “edgy” thoughts together and what you get is insight and understanding.
Study may explain counterintuitive effect of why hotter systems can cool more quickly
October 23, 2017 by Lisa Zyga
In the last few decades, the Mpemba effect has been studied and observed in several physical systems besides water, including carbon nanotube resonators and ice-like water cages called clathrate hydrates. Despite these findings, the causes of the effect are not well-understood. Proposed explanations include the presence of impurities, hydrogen bonding, and supercooling. Even the mere existence of the Mpemba effect remains controversial, as one recent study found insufficient evidence to replicate a meaningful effect.
Now, their interest rekindled by a recent paper proposing a generic mechanism for similar effects, scientists Antonio Lasanta and coauthors from universities in Spain have returned to the question in a new study published in Physical Review Letters. In their work, the researchers theoretically demonstrate and investigate the Mpemba effect in granular fluids, such as those made of sand or other small particles.
Lisa writes really well, and it would be a nice thing to ‘hit the link’ and read the whole article. It’s a bit difficult to remove parts of the article from the quotes and not spoil the flow of the writing as she has already edited it to a tight text. In the original the word “paper” links to here:
Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse
Zhiyue Lua,1,2 and Oren Razb,1,2
Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved April 4, 2017 (received for review January 23, 2017)
It is commonly expected that cooling a hot system takes a longer time than cooling an identical system initiated at a lower temperature. Surprisingly, this is not always the case; in various systems, including water and magnetic alloys, it has been observed that a hot system can be cooled faster. These anomalous cooling effects are referred to as “the Mpemba effect”, and so far they lack a generic details-independent explanation. Based on recent developments in the theory of nonequilibrium thermodynamics, we propose a generic mechanism for similar effects, demonstrate it in various systems, and predict a similar anomalous behavior in heating.
Under certain conditions, it takes a shorter time to cool a hot system than to cool the same system initiated at a lower temperature. This phenomenon—the “Mpemba effect”—was first observed in water and has recently been reported in other systems. Whereas several detail-dependent explanations were suggested for some of these observations, no common underlying mechanism is known. Using the theoretical framework of nonequilibrium thermodynamics, we present a widely applicable mechanism for a similar effect, the Markovian Mpemba effect, derive a sufficient condition for its appearance, and demonstrate it explicitly in three paradigmatic systems: the Ising model, diffusion dynamics, and a three-state system. In addition, we predict an inverse Markovian Mpemba effect in heating: Under proper conditions, a cold system can heat up faster than the same system initiated at a higher temperature. We numerically demonstrate that this inverse effect is expected in a 1D antiferromagnet nearest-neighbors interacting Ising chain in the presence of an external magnetic field. Our results shed light on the mechanism behind anomalous heating and cooling and suggest that it should be possible to observe these in a variety of systems.
Full text here:
I’ll leave it for those interested to read the full text as it has a fair number of graphics in it and lots of formulas that don’t quote well / easily. (Lots of unicode needed to get it right). Back at the phys.org article…
Using simulations of granular systems and a simple kinetic theory approach, the researchers were able to determine that the initial conditions in which the system is prepared play a critical role in determining whether or not the system exhibits the Mpemba effect. Their analysis also enabled them to identify the initial conditions required in order for a granular system to exhibit the Mpemba effect.
“Our work shows that the existence of the Mpemba effect is very sensitive to the initial preparation of the fluid or, in other words, to its previous history,” coauthor Andrés Santos at the University of Extremadura in Badajoz, Spain, told Phys.org. “In our opinion, this may explain the elusiveness and controversy of the Mpemba effect in water, as a consequence of the lack of control on the detailed initial preparation of the sample.”
As the researchers showed, if a system is not prepared under certain initial conditions, then the colder system cools down more quickly than the warmer one, as expected, and there is no Mpemba effect.
“We theoretically showed, at least in the case of a gas, that a system’s temperature evolution and thus its cooling and/or heating rate do not depend on initial temperature alone, but also on the previous history of the system that control the initial value of the additional variables,” Santos said. “Therefore, it is perfectly possible that an initially heated system cools down quicker than a colder one with a different history.”
As the researchers explained further, the simplicity of the Mpemba effect in granular fluids compared to water and other systems enabled them to reach this conclusion.
“Our results show that the Mpemba effect is a generic non-equilibrium phenomenon that appears if the evolution of temperature depends on other physical quantities that characterize the initial state of the system,” Santos said. “In practice, such an initial state can be experimentally achieved if the system is taken by some physical procedure very far away from equilibrium (for instance, by a sudden heating impulse prior to cooling down). Our theoretical and computational work shows that the Mpemba effect is particularly simple in a granular gas, since, in practice, there is one single extra parameter controlling the Mpemba effect. This parameter is the kurtosis, which measures the deviation of the velocity distribution function from a Gaussian distribution.”
Guess what every climate model does NOT include… The Mpemba Effect and the history of the state of water in the system. They ignore kurtosis at all levels, but completely omit it at the level of water thermodynamics.
The results also support predictions of the existence of an inverse Mpemba effect: when heated, a colder sample may reach a hot target temperature sooner than a warmer sample. The researchers plan to investigate this area and others in the future.
“On the theoretical side, we plan to carry out a similar study in the case of a molecular solute (where collisions are fully elastic) suspended in a solvent that produces a nonlinear drag force on the solute particles,” Santos said. “Going back to granular fluids, we also want to analyze the impact of particle roughness and spin on the Mpemba effect. In the latter system, the simplest model would couple the temperature evolution to that of the parameter measuring the non-equipartition of energy between the translational and rotational degrees of freedom.
Gee, wonder if that might have anything to do with the sticky problem of cloud formation… are clouds a “molecular solute” suspended in a solvent (air) with nonlinear drag forces? What about dust in air and cloud formation?
So just how “settled” is this “settled science” for clouds, ice, our whole water world?