Frank Wilczek's time crystals are now in Wikipedia:

https://en.wikipedia.org/wiki/Space-time_crystal
"A time crystal or space-time crystal is an open system in non-equilibrium with its environment that exhibits time translation symmetry breaking (TTSB). It is impossible for a time crystal to be in equilibrium with its environment. The idea of a time crystal was first put forward by Nobel laureate and MIT professor Frank Wilczek in 2012. Space-time crystals extend the ordinary three-dimensional symmetry seen in crystals to include the fourth dimension of time; a time crystal spontaneously breaks the symmetry of time translation. The crystal's pattern repeats not in space, but in time, which remarkably allows for the crystal to be in perpetual motion."

Frank Wilczek is an admirer of beauty, not rationality, so he probably sees no reason why the following question should be asked, let alone answered:

Do time crystals exchange energy with the surroundings, and if they do, what kind of energy is that?

Until this question is clearly answered, the time crystal story will be just another means to brainwash the gullible world (Frank Wilczek and his brothers Einsteinians are very experienced in this).

Pentcho Valev