It is interesting to look at the situation in the TGD framework. From the abstract of the article also from the Wikipedia article about time crystals one learns that the system has periodic energy feed and is therefore not closed so that the finding is not in conflict with the second law and perpetuum mobile is not in question.
1. What is time crystal?
The notion of time crystal (this) is a temporal analog of ordinary crystals in the sense that there is temporal periodicity, was proposed by Frank Wilczeck in 2012. Experimental realization was demonstrated in 2016-2017 but not in the way theorized by Wilczek. Soon also a no-go theorem against the original form of the time crystal emerged and motivated generalizations of Wilzeck's proposal.
The findings reported by Google are however extremely interesting. Very concisely, researchers study a spin system, which has two directions of magnetization and the external laser beam induces the system to oscillate between the two magnetization directions with a period, which is a multiple of the period of the laser beam. It is interesting to consider the system in TGD framework and I have actually discussed time crystals briefly in a recent article.
2. Space-time surfaces as periodic minimal surfaces as counterparts of time crystals
In TGD, classical physics is an exact part of quantum theory and quantum classical correspondence holds true. Hence it is interesting to consider first the situation at the classical space-time level. In TGD time crystals have as classical correlates space-time surfaces which are periodic minimal surfaces.
It is possible to have analogs of time-crystals and also more general structures built as piles of lego like basic pieces in time direction bringing in mind sentences of language and DNA, which is quasi-periodic structure and more general than crystal.
3. What about thermodynamics of time crystals?
Could the time crystal be possible also in thermodynamic sense and even for thermodynamically closed systems? In TGD Negentropy Maximization Principle (NMP) (see this) and zero energy ontology (ZEO) (see this and this) forces to generalize thermodynamics to allow both time arrows. ZEO is forced by TGD inspired theory of consciousness and solves the basic paradox of quantum measurement theory. The arrow of time would change in ordinary ("big") state function reduction (BSFR) and would remain unaffected in "small" SFR (SSFR). Second law holds true at the level of real physics but in the cognitive sector information increases and NMP holds true.
4. Is new quantum theory making possible quantum coherence in long scales needed?
Also new quantum theory might be needed to explain why the period is multiple of the driving period. The first possibly needed new element is hierarchy of effective Planck constants heff= n×h_0 having number theoretical interpretation. heff measures the scale of quantum coherence and has also interpretation as the order of Galois group for a polynomial defining the space-time surface in M8 mapped to M4×CP2 by M8-H duality (see this and this).
The replacement of h with heff scales the periods by n and keeps energies unchanged. In TGD inspired biology heff hierarchy is in a crucial role and its levels behave relative to each other like dark matter.
In the recent case, the magnetic body (MB)of the spin system controlling its behavior would have heff=nh. Each period would be initiated by BSFR at the level of MB and change the arrow of time and induce effective change of it also at the level of the ordinary matter.
In ZEO, time crystal-like entities, which live in cycle by extracting back part of the energy that they have dissipated in a time reversed mode, are in principle possible. System "breathes". Various bio-rhythms could correspond to time crystals. The biological analogy is obvious and we know that life requires a metabolic energy feed: in TGD Universe it prevents the decrease of heff (see this).
5. Perpetuum mobile?: almost but not quite!
For an thermodynamically open system, part of the dissipated energy leaks into the external world during each half cycle. Same happens in the time reversed mode and would mean that the system apparently receives positive energy also from the external world. Could this energy feed compensate for the energy loss to the external world by dissipation so that no external energy feed would be needed? Perhaps this might be the case in the ideal situation.
One would have almost a perpetuum mobile! Periodic driving feeding energy to the system would be needed to take care that heff is not reduced.
See the chapter Quantum Criticality and Dark Matter: part II.
For a summary of earlier postings see Latest progress in TGD.