Coexistence of Synchronization and Stochasticity in Thermally Coupled Mott Oscillators

Synchronization is conventionally regarded as a mechanism for suppressing variability and enforcing order in coupled systems, from pendula and lasers to neurons and electronic oscillators. Here, we show that synchronization can also embed stochasticity at finer scales. We observe this phenomenon in thermally coupled VO₂ neuristors, where robust in-phase synchronization at the microsecond scale coexists with spike onset fluctuations at the nanosecond scale, with no fixed leader. The coexistence of order and disorder originates from stochastic domain-level physics of the insulator-metal and metal-insulator transitions, where local variations in transition temperature drive cycle-to-cycle randomness in nucleation, percolation, and relaxation. A stochastic domain model reproduces this effect by generating synchronized spike trains with random lead-lag jitter, and experimental interspike interval statistics confirm the persistence of fine-scale variability despite macroscopic phase locking. These findings establish that synchronization and stochasticity can coexist within the same physical platform, revealing hidden disorder within collective order. This insight reframes synchronization as not purely deterministic, but as a universal context where microscopic variability can persist, with implications for electronics, cryptography, and the fundamental physics of order-disorder coexistence.