Comment: Feedback Physics World  March 2018

Climate hop

In response to Jennifer Ouellette’s feature “When cold warms faster than hot” (December 2017) in which she describes what could be a new theoretical understanding for the so-called Mpemba effect – and why it predicts that cold water could even heat up faster than warm water.


Some years ago, one of my ablest students investigated the Mpemba effect for his extended essay, as part of his International Baccalaureate Diploma. Consistent with others, the results of his excellent investigation were inconclusive. Convection-induced supercooling looked the most convincing mechanism at the time. He performed his experiment in a domestic refrigerator and I did wonder whether supercooling might have been thwarted whenever the thermostatically-controlled pump switched on or off, with freezing induced by the vibration.

With my interest piqued, I found the excellent article by Ouellette so absorbing that I chased down all the papers referenced. The paper by Zhiyue Lu and Oren Raz on the Markovian Mpemba effect brought to mind my undergraduate project when I used an electronic circuit to investigate whether stochastic resonance might be responsible for the glacial-interglacial hopping of our climate throughout the present Pleistocene ice age. Our climate was modelled as having two stable states, with a ‘particle’ sitting in a symmetric double-well or ‘Mexican hat’ potential. Changes in our orbit (eccentricity, obliquity, precession) described by the Milankovitch Effect was modelled as a sinusoidal forcing of the potential, which made it see-saw about the potential barrier, but nowhere near enough to induce the particle to hop. But the introduction of some Gaussian white noise over a narrow range of power spectral density made the particle (the climate) hop in a periodic way, leading to the counter-intuitive observation that the signal (periodic hopping) increased in response to an increase in noise. Since I left research for teaching two decades ago, accessible feature articles in Physics World are a very welcome way of keeping abreast of developments.

Mike Follows

Acting head of physics, King Edward’s School, Birmingham, UK