The Irreversible Unitary

Quantum mechanics is unitary — information is preserved, evolution is reversible. Thermodynamics is irreversible — systems relax, entropy increases, correlations decay. The tension between these two statements is foundational. How does irreversibility emerge from reversible microscopic dynamics?

Yoshimura and Sá (arXiv:2501.06183) show that in generic quantum many-body systems without conservation laws, the Ruelle-Pollicott resonances — poles that control the decay of correlations — all converge inside the unit disk as the system size grows. This means that every correlation function decays exponentially, even though the underlying evolution is perfectly unitary. Irreversibility isn’t imposed from outside; it’s a spectral property that emerges in the thermodynamic limit.

The demonstration uses the random phase model — a Floquet quantum circuit — where the result can be proven analytically as local Hilbert space dimension grows. But the structural claim is broader: unitarity guarantees information preservation globally while the resonance structure guarantees that no local observable can access that information. The information isn’t lost. It’s redistributed across exponentially many degrees of freedom, and the time to recover it exceeds any physical timescale.

The key technical finding is the two-stage relaxation of out-of-time-order correlators: a fast initial decay controlled by the leading resonance, followed by a slower approach to the ergodic value. Irreversibility has structure — it’s not a single exponential but a hierarchy of timescales, each controlled by a different resonance.

Reversibility is exact and irrelevant. Irreversibility is approximate and real.