The thermodynamic uncertainty relation (TUR) establishes a tradeoff: the precision of a current measurement (inverse relative variance) is bounded by the entropy production. More precise measurements require more dissipation. The relation is universal for classical Markovian systems — no process can beat the bound.
Quantum collisional models break it. In these models, a system interacts sequentially with auxiliary particles (an “environment” built one collision at a time). The TUR violations depend on the dynamics: Markovian, weakly non-Markovian, or strongly non-Markovian.
The violation patterns differ. In some regimes, the maximum violation occurs at steady state — the system permanently exceeds the classical bound. In others, the violation is necessarily transient, appearing only at early times before the system relaxes to a state that respects the bound. The type and degree of non-Markovianity — how much memory the environment retains — controls which pattern appears.
The mechanism: quantum coherence creates correlations between successive measurements that the classical TUR does not account for. The classical bound assumes that current fluctuations and entropy production are independent enough that precision cannot exceed the dissipation budget. Quantum coherence couples them, allowing the system to extract more precise information per unit of entropy produced.
The structural point: the thermodynamic uncertainty relation is a property of classical dynamics, not of thermodynamics itself. Quantum systems access a regime where precision is cheaper than the classical bound predicts. The tradeoff is real but looser than thought — and the looseness depends on memory (non-Markovianity), not just on quantumness.