Anomalous relaxation and Mpemba effects

6 problems

• Strong Mpemba effect in interacting many-particle colloidal systems

  Open

  Exponentially faster cooling has been seen for one microscopic bead moving in a carefully shaped energy landscape. The question is whether the same effect exists, and can be measured, for many interacting beads, where the slowest relaxation is collective.

• Universal scaling of direct and inverse Mpemba effects near criticality

  Open

  Near a phase transition (such as a magnet losing its magnetization at a critical temperature), relaxation becomes slow and governed by a few universal numbers. The question is whether the existence and timing of Mpemba effects there are also fixed by those universal numbers.

• Experimental observation of the Mpemba effect in a granular gas

  Open

  A granular gas (many grains bouncing and losing energy in each collision) is predicted to show a hotter sample cooling below a target temperature before a cooler one, if the hot sample's speed distribution has the right shape. No experiment has yet confirmed this.

• Necessary and sufficient conditions for the Markovian Mpemba effect

  Partially resolved

  In simple models where a system hops randomly between a few states, a hotter start can lose the overlap with the slowest-decaying pattern and so cool faster. The task is to state exactly which energy landscapes allow this.

• General criterion for the quantum Mpemba effect in symmetry restoration

  Partially resolved

  In some quantum spin chains, a state that breaks a symmetry more strongly at the start regains that symmetry faster in a small region than a weakly broken one. The task is a general rule, valid beyond special solvable models, for when this happens.

• Does hot water reproducibly freeze before cold water

  Contested

  The claim that hot water freezes faster than cold water is old and widely repeated, but careful experiments disagree on whether it is real. The question is whether, under controlled conditions, it happens reliably and for what reason.