A “speed limit” on changes in non-equilibrium systems that was first predicted in 2020 has been confirmed by a new experiment done in China. By carefully controlling the electronic states of a single trapped ion, a team led by Mang Feng at the Chinese Academy of Sciences in Wuhan, showed that the rate at which entropy was created during electronic transitions was intrinsically linked to the speed at which the transition occurred. Their discovery could lead to a better understanding of systems as diverse as living organisms and quantum computers.
The dissipation of heat is an important aspect of every process in nature. No real thermodynamic system, be it a living organism or an industrial process, exists in a state of equilibrium. Instead, energy continually flows through systems and the second law of thermodynamics requires that some of it is dissipated as waste heat – thereby increasing the overall disorder (or entropy) of the universe.
In 2020, physicists Gianmaria Falasco and Massimiliano Esposito, both at the University of Luxembourg, established a mathematical relationship between changes occurring to non-equilibrium systems, and the heat they dissipate in the process.
Dissipation–time uncertainty relation
The duo established that the rate at which heat is dissipated in a non-equilibrium process multiplied by the time taken by the process can never be smaller than the Boltzmann constant. This is reminiscent of Heisenberg’s uncertainty principle in quantum mechanics, so they called it the “dissipation–time uncertainty relation”. The upshot is that faster changes in non-equilibrium systems will inevitably lead to higher rates of heat dissipation (and entropy production).
To test this theory, Feng’s team developed a highly simplified set-up containing a single calcium atom, confined in an electromagnetic trap. When excited to a higher-energy state by a laser, the atom will subsequently decay back to its original lower-energy state. Falasco and Esposito’s proposal predicts that if the decay rate of the excited state could be reduced, this should be accompanied by a lower rate of energy dissipated from the system.
Cold and hot baths
To measure this dissipation, Feng and colleagues used laser light to excite the ion to several other states. Some of these states behaved like a “cold bath” and accepted dissipative energy from the ion in the excited state of interest. Other states behave like a “hot bath” and dissipated energy into the excited state. In this way the decay resembled a more complex non-equilibrium process with energy flowing through it.
How entropy might increase backwards in time – as well as forwards
By tracking the state of the ion over time, Feng’s team could then measure both the time taken for its excited state to decay, and the average amount of heat dissipated during this jump. For the first time, their findings confirmed Falasco and Esposito’s predictions experimentally. They observed that longer decay times were usually associated with less dissipative decay pathways.
Further studies of the dissipation–time uncertainty relation could shed light on a wide range of non-equilibrium processes including the function of living organisms and the operation of quantum computers.
The research is described in Physical Review Letters.
