Physicists proved a universal quantum speed limit for thermalization in a paper published in Nature Physics. Researchers used quantum information theory to show that quantum mechanics sets a boundary on how fast systems reach equilibrium. The authors wrote, "the thermalization machine cannot violate the Heisenberg limit," confirming this fundamental speed limit.
Whether we are waiting for a car windshield to defrost in winter or a warm drink to cool down, how long it takes for an object to settle into a stable, even temperature within its environment (thermal equilibrium) depends on numerous factors. These can include surface area, the material properties of an object and airflow.
But when we zoom down to the subatomic scale, such as where qubits operate in a quantum computer, a different set of rules takes over. External conditions still matter, but according to a new paper published in the journal Nature Physics, quantum mechanics sets a fundamental speed limit on how quickly a process can bring different quantum systems into thermal equilibrium.
What makes the finding significant is that this boundary is universal. No matter how much energy is applied or how strongly a system is manipulated, the process cannot be forced to go any faster.
The search for a universal speed limit
For years, physicists had observed hints of this Planckian limit in superconductors and quantum systems, leading them to suspect a universal speed limit existed. But a general mathematical proof establishing such a limit was missing.
Step forward Paolo Abiuso at the Austrian Academy of Sciences and his colleagues.
The researchers created a universal mathematical framework that treats thermalization as a process capable of bringing different quantum systems into their corresponding thermal states. They used quantum information theory to calculate how quickly this can happen under the laws of quantum mechanics.
To illustrate their findings, the team applied their equations to a theoretical model of interacting quantum particles and examined its behavior mathematically.
A speed limit that cannot be broken
So what did all that number crunching and theorizing result in?
The team showed that quantum mechanics sets a speed limit on bringing different quantum systems into thermal equilibrium. They discovered that this limit is determined by temperature and two fundamental constants of nature, the reduced Planck constant and Boltzmann's constant.
"In other words, this bound follows from the observation that the thermalization machine cannot violate the Heisenberg limit [a fundamental limit on how precisely quantum properties can be measured]," the study authors wrote.
This means that at higher temperatures, the minimum time needed for quantum systems to reach thermal equilibrium can be shorter, but they still cannot breach this fundamental speed limit when it applies. Their findings confirm that this speed limit depends on temperature and quantum mechanics, regardless of how complex the surrounding environment might be.
However, at extremely low temperatures, the energy difference between a system's two lowest energy states determines the limit instead.
The paper is much more than clever math. Understanding these universal speed limits could help researchers develop quantum technologies, including better quantum computers.