Consider a quantum thermalization process that, for a set of distinct Hamiltonians, prepares states close to the corresponding thermal ensembles at temperature T. The Planckian thermalization problem asks whether there is a universal lower bound on the thermalization time tau, independent of the details of the system, namely tau≥ fractau_Pl2=frachbar2k_BT. In the low-temperature regime, where the relevant energy scale is the spectral gap Delta between the ground and first excited states, the corresponding bound is tau≥ frachbarDelta; the regimes are characterized by beta Deltalesssim 1 and beta Delta≫ 1, respectively, with beta=(k_BT)^-1.

Planckian bound for thermalization

Consider a quantum thermalization process that, for a set of distinct Hamiltonians, prepares states close to the corresponding thermal ensembles at temperature $T$ . The Planckian thermalization problem asks whether there is a universal lower bound on the thermalization time $\tau$ , independent of the details of the system, namely $\tau\geq \frac{\tau_{\mathrm{Pl}}}{2}=\frac{\hbar}{2k_{\mathrm{B}}T}$ . In the low-temperature regime, where the relevant energy scale is the spectral gap $\Delta$ between the ground and first excited states, the corresponding bound is $\tau\geq \frac{\hbar}{\Delta}$ ; the regimes are characterized by $\beta\Delta\lesssim 1$ and $\beta\Delta\gg 1$ , respectively, with $\beta=(k_{\mathrm{B}}T)^{-1}$ .

References

Primary source

Nature Physics

Additional references

An information-theoretic proof of the Planckian bound for thermalization — Nature Physics — Paolo Abiuso, Alberto Rolandi, John Calsamiglia, Pavel Sekatski, Martí Perarnau-Llobet

quantum-information quantum-metrology quantum-statistical-mechanics

Posted 1 week ago · edited 1 week ago

Progress summary

Refreshed 1 week ago

Claimed solved

A 2025 paper claims to prove a universal lower limit on how quickly systems can reach thermal equilibrium, with a different limit at very low temperature.

The problem concerns a general lower bound on thermalization time. Abiuso, Rolandi, Calsamiglia, Sekatski, and Perarnau-Llobet claim an information-theoretic derivation in a June 2025 preprint.

Information-theoretic proof, June 2025

The authors claim that, for their operational notion of thermalization, $\tau \ge \tau_{\rm Pl}/2$ when $\beta\Delta\lesssim 1$ , with $\tau_{\rm Pl}=\hbar/(k_{\rm B}T)$ , and $\tau\ge\hbar/\Delta$ when $\beta\Delta\gg 1$ . The argument uses Hamiltonian estimation, quantum information geometry, and metrology, and connects the bound to the adiabatic theorem. The claim is reported in a Nature Physics article but remains unverified here.

Current status (as of September 2026): The operational thermalization bound is claimed in a preprint and Nature Physics article, while broader interpretations of a universal Planckian timescale and independent verification remain open.

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