What substance will have the largest specific heat capacity integrated from T=0 to, say, room temperature? In other words, given a finite amount of mass, what object or collection of objects has the largest number of degrees of freedom that can be excited as it absorbs energy starting from T=0? Would it be a complicated molecular polymer that can be tangled in all sorts of ways, or some kind of gas of low-mass particles, or maybe a spin lattice of some sort? Is there some kind of fundamental limit in the universe of the number of quantum degrees of freedom per mass or perhaps per volume that is allowed?
(1) If you allow a very long time for the substance to warm up, go with a kilogram of $\nu_1$, the lightest neutrino.
(2) If you require that the substance heat up using electromagnetism (i.e. photons), then go with a kilogram of electrons.
(3) If you also require that the substance be electrically neutral and not decay, then a kilogram of hydrogen will fit the bill.
(4) If you further require that the substance be chemically stable, then molecular hydrogen is almost as good.
The reason these are the answers is because they have the lightest weights. So they have more degrees of freedom per kilogram.
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