Physicists at the Austrian Academy of Sciences, Universitat Autònoma de Barcelona, and the University of Geneva have proven at a quantum level what others had long suspected – that quantum mechanics imposes a speed limit on how fast a system with a temperature difference among its components reaches thermal equilibrium. This speed limit is universal, and nothing one does to the system can actually change it. Thermal equilibrium might sound like a tough concept, but hundreds of systems reach them around us on a daily basis. A hot cup of coffee will eventually cool down to room temperature, or a glass of cola will also become warm to reach about the same temperature, even if they are not kept in close proximity to each other. How quickly this occurs can depend on external factors like the temperature of the room or how big a glass of drink you have poured, etc. But physicists have long suspected that at a subatomic level, there is a something that inherently controls how fast these changes can occur.A team of researchers from some of the top institutes in Spain, Austria and Switzerland have now arrived at mathematical proof that shows that there is indeed a quantum-level speed limit that determines how quickly systems reach their thermal equilibrium. Arriving at the proofEven though we may not have noticed this in our cooling cup of coffee, physicists have long noticed the likelihood of a speed limit when working with superconductors and other quantum systems. To demonstrate that it really exists, scientists need a mathematical proof, which is exactly what the European researchers set out to do. Using a universal mathematical framework, the researchers treated thermalization as a process that can bring different quantum systems into their corresponding thermal states. Using quantum information theory, they also determined how quickly this could be achieved based on quantum-mechanical principles. They then applied their equations to a theoretical model of quantum particles and attempted to analyze their behavior mathematically. The analysis showed that quantum mechanics does indeed put a speed limit on how quickly different quantum systems can reach a thermal equilibrium. A universal limitThe researchers found that the limit is not only determined by the temperature of the system but also by two constants – the reduced Planck’s constant and the Boltzmann constant, which relates the average kinetic energy of particles in a gas to the thermodynamic temperature of the system. This means that even when system components may be at higher temperatures and seem to reach equilibrium quickly, they still cannot go faster than the speed limit imposed by quantum mechanics. This confirms that the speed limit depends on the temperature and quantum mechanics and not the complexity of the environment it is operating in. Interestingly, though, when system components have very little temperature difference, the rate of thermal equilibrium is not the same as when the temperature differences are on the higher side. Instead, this is determined by the two lowest-energy states in the system. The findings open up new research avenues in quantum technologies such as computing and sensing. The research findings were published in the journal Nature Physics.