text: Time crystals seem to break time-translation symmetry and have repeated patterns in time even if the laws of the system are invariant by translation of time. The time crystals that are experimentally realized show discrete time-translation symmetry breaking, not the continuous one: they are periodically driven systems oscillating at a fraction of the frequency of the driving force. (According to Philip Ball, DTC are so-called because "their periodicity is a discrete, integer multiple of the driving period".)
  The initial symmetry, which is the discrete time-translation symmetry () with , is spontaneously broken to the lower discrete time-translation symmetry with , where  is time,  the driving period,  an integer.
  Many systems can show behaviors of spontaneous time-translation symmetry breaking but may not be discrete (or Floquet) time crystals: convection cells, oscillating chemical reactions, aerodynamic flutter, and subharmonic response to a periodic driving force such as the Faraday instability, NMR spin echos, parametric down-conversion, and period-doubled nonlinear dynamical systems.
  However, discrete (or Floquet) time crystals are unique in that they follow a strict definition of discrete time-translation symmetry breaking:
  * it is a broken symmetry the system shows oscillations with a period longer than the driving force,
  * the system is in crypto-equilibrium these oscillations generate no entropy, and a time-dependent frame can be found in which the system is indistinguishable from an equilibrium when measured stroboscopically (which is not the case of convection cells, oscillating chemical reactions and aerodynamic flutter),
  * the system exhibits long-range order the oscillations are in phase (synchronized) over arbitrarily long distances and time.
  Moreover, the broken symmetry in time crystals is the result of many-body interactions: the order is the consequence of a collective process, just like in spatial crystals. This is not the case for NMR spin echos.
  These characteristics makes discrete time crystals analogous to spatial crystals as described above and may be considered a novel type or phase of nonequilibrium matter.