Phantom degeneracy are degenerate states that a system can take but cannot be occupied, thus it does not contribute to the expectation value of the energy of a system. One can detect their presence by finding the system sometimes is described by the state variables taking a certain set of values, hence suggesting the presence of extra degenerate states in the system to describe it, but the energy distributions were found to agree with as if these states never existed in the system.
They are extremely unusual states that exists in some special matter, and they are frequently used to power engines exploiting the Second Law of Thermodynamics without a loss in efficiency (since energy never get partitioned into them, despite the system do explore them at equilibrium, thus entropy still increases).
In real life[]
No sorry, these things don't exist, please do not waste time trying to circumvert the inefficiency problem that is the consequence of the second law of thermodynamics.
A weaker version?[]
https://www.sciencedaily.com/releases/2017/02/170202145840.htm
However, perhaps engineering a heat sponge might be possible by taking reference of the findings here, and exploiting certain nanostructures to massively increase the number of microstates relative the the local environment so heat and some molecules with matching high entropic configurations are preferentially partitioned into it due to entropy.
While this will allow semi efficient absorption of heat, the high entropy of the system means it will be very inefficient to reverse it, raising the question on whether it is useful in the first place.