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[Sowelu]

How much energy are we talking about here; enough that quantum effects might kick in?  Because I could imagine that over vast, vast, tremendously huge amounts of time...oh, a kalpa or two...you'd end up with the same energy in the system, but the ice crystals would be evenly distributed throughout the liquid water (with the same amount of crystallization bonds).  You'd kick in just enough energy from the quantum chaos, that energy would be taken out somewhere else, something melts, another thing freezes, the energy remains constant.

[Virex]

I don't think that'd work. Distributing the ice crystals would reduce the entropy of the system since there's more surface area in the liquid. You'd be breaking the second law.

[Osmosis Jones]

It's already been pointed out earlier that it takes energy, but here's the maths behind it;

-Q = m.C₁.ΔT₁ + m.L_f + m.C₂.ΔT₂

That is the energy required to change a mass m of something from some temperature ΔT₁ above freezing point, through the phase change (with a latent heat of fusion L_f), to some temperature ΔT₂ below freezing. Or vice versa; the equation is general. The important factor for this discussion is of course -Q_freezing = m.L_f, which the above reduces to if we assume everything is at 0^oC already.