Quantum mechanics fundamentally limits how quickly things can reach equilibrium, according to a new theoretical result from the Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, together with colleagues from TU Wien, the Universitat Autònoma de Barcelona (UAB) and the University of Geneva. Researchers established a minimum timescale for thermalization, the process by which a system approaches thermal equilibrium, defined by the Planck constant, the Boltzmann constant, and the target temperature.

At finite temperature, the minimum timescale is set by one half of the Planckian dissipation time. “The key idea came from a rather unexpected field: quantum metrology,” says Martí Perarnau-Llobet, working at Universitat Autònoma de Barcelona, as the team approached the problem as an information-processing challenge.

This establishes a quantifiable limit on how rapidly thermalization can occur, independent of the material or its interactions. At very low temperatures, however, the relevant timescale shifts; the limit becomes defined by ℏ/Δ, where Δ represents the energy gap between the ground and first excited states. This temperature dependence highlights that the quantum limit on thermalization isn’t a single value, but a dynamic constraint that adjusts to the system’s energy level.

The team constructed a specifically engineered thermalization machine that achieves this theoretical limit for a defined pair of Hamiltonians, demonstrating the bound is not merely a theoretical construct. Considering thermalization as an information-processing task proved essential to this discovery; the team leveraged concepts from quantum information geometry and quantum metrology to establish the universal constraint.

The key idea came from a rather unexpected field: quantum metrology.
Martí Perarnau-Llobet, working at UAB

The minimum time for a system to reach thermal equilibrium isn’t arbitrary; it’s fundamentally constrained by the Planckian dissipation time for sufficiently mixed thermal states, a figure derived from fundamental constants. Researchers established this bound not by modeling specific materials, but by considering a theoretical operating under strictly quantum mechanical rules. This hypothetical device, capable of preparing diverse thermal states, reveals a fundamental constraint on how quickly any physical system can thermalize, regardless of its composition.

The emergence of the Planckian timescale, originally observed in the resistivity of superconductors, across diverse quantum phenomena suggests a deeper connection between dissipation and fundamental quantum limits. Jan Zaanen first coined the term “Planck scale of dissipation” in 2004, noting its apparent universality, and subsequent models linked it to the rate of chaos in many-body systems.

Establishing a universal bound proved difficult, as engineered interactions can rapidly prepare known thermal states, sidestepping the need for a true limit. This new approach, however, focuses on the machine’s ability to create any thermal state, not just a predetermined one, revealing a structural reason for the timescale’s persistence. At extremely low temperatures, the ℏ/Δ bound connects to the quantum adiabatic theorem, suggesting a unified framework for understanding thermalization across a broad range of conditions.