Crypto-equilibrium is the condition, described in the source dossier, in which a discrete time crystal's oscillations generate no entropy and a time-dependent frame can be found in which the system is indistinguishable from equilibrium when measured stroboscopically.
Role in the definition of a discrete time crystal
The dossier lists crypto-equilibrium as one of three strict criteria distinguishing discrete (or Floquet) time crystals from other systems showing spontaneous time-translation symmetry breaking:
- Broken symmetry — the system shows oscillations with a period longer than the driving force.
- Crypto-equilibrium — the oscillations generate no entropy, and a time-dependent frame can be found in which the system is indistinguishable from equilibrium when measured stroboscopically.
- Long-range order — the oscillations are in phase (synchronized) over arbitrarily long distances and time.
The dossier states explicitly that crypto-equilibrium is not satisfied by convection cells, oscillating chemical reactions and aerodynamic flutter. This is the criterion that separates a genuine discrete time crystal from a driven system that merely oscillates.
Relation to thermodynamics
The dossier's thermodynamics section states that time crystals do not violate the laws of thermodynamics: energy in the overall system is conserved, such a crystal does not spontaneously convert thermal energy into mechanical work, and it cannot serve as a perpetual store of work. It may, however, "change perpetually in a fixed pattern in time for as long as the system can be maintained." The source uses the phrase "motion without energy" — the apparent motion does not represent conventional kinetic energy — and states that a time crystal's entropy stays constant over time, which "barely satisfies the second law of thermodynamics by not decreasing."
Related work
- Discrete Time Crystal (DTC) — the regime in which crypto-equilibrium is a defining criterion.
- Spontaneous Time-Translation Symmetry Breaking — the underlying mechanism.
Source notes & attribution
- https://rexresearch.com/WilczekTimeCrystals/WILCZEKTimeCrystals.html