Jonathan Oppenheim, a quantum physicist at University College London, in the UK, says we are standing on the brink of our third great revolution in thermodynamics.

The eighteenth century saw the development of the steam engine and the industrial revolution, built on advances in thermodynamics—the science of heat and energy transfer. The twentieth century saw the discovery of new laws that govern the microscopic realm, quantum mechanics. That led to the invention of the transistor and, in turn, today’s digital revolution. But what further advances could we make if were able to combine both of these into one theory of "quantum thermodynamics"?

"The systems we are building are getting smaller and smaller," says Oppenheim. Nanoscale devices, biological motors and quantum computers are just some of the tiny technologies we are trying to perfect. How does thermodynamics work on this quantum level? Oppenheim has recently been awarded an FQXi grant of over $60,000 to investigate.

Oppenheim was inspired to think about quantum mechanics from a thermodynamical perspective during his PhD at the University of British Columbia, in Vancouver, when he read a book by Nobel Laureate physicist Richard Feynman on computation. "For me it was this really beautiful thing and I became really interested in the interplay between information theory and thermodynamics," says Oppenheim.

The second law of thermodynamics is notorious. It places a restriction on the direction of heat flow in a closed system—namely that heat will not spontaneously flow from a cold object to hot object. It is why, unfortunately, cold cups of coffee never magically reheat themselves. It says the entropy (disorder) of a closed system always increases. Another way of describing the consequences of the second law is that you cannot create a heat engine which extracts heat and converts it all to useful work.

A theory of quantum thermodynamics could similarly uncover limits on the amount of useful work that can be gained from atomic scale devices. The conventional, macroscopic rules of thermodynamics represent a statistical approach looking at the overall behaviour of many atoms or molecules at a time. Oppenheim is investigating whether such macroscopic rules can be applied to a microscopic system too, and, if so, whether the rules of thermodynamics for a single particle is the same as for an ensemble of many.

Free Energy

"It turns out there are rules of thermodynamics for quantum systems," says Oppenheim. Rather than thinking of the second law as the notion that entropy always increases in a closed system, Oppenheim prefers to picture it as stating that the "free energy" always decreases. The free energy is the amount of useful energy in a system that is free to do work. "There are many free energies that all have to go down, but in a macroscopic system they are all equivalent. So you can think of it as a single free energy," he says.

Crucially, Oppenheim’s work with others has shown that you cannot play the same trick in a quantum regime. The range of free energies are all different and they all have to decrease in order to satisfy the second law (PNAS 112, 3275 (2015)). His task now is to fully formulate these laws.

Oppenheim’s work on how the other laws of thermodynamics apply in the quantum regime could be just as important. Take the third law, for example. "It says that it takes an infinite amount of time to cool something to absolute zero," says Oppenheim. With many quantum technologies—including quantum computing—you want to be able to cool the system as much as possible, but the third law provides a restriction. "We can use our techniques to get a more quantitative and robust answer to how cool we can get a system of a few molecules if we only have a certain amount of time," he says.

Matt Leifer, an FQXi member and physicist at the Perimeter Institute for Theoretical Physics in Ontario, Canada, sees this as important work. "It ties together a number of threads that are becoming increasingly important for our understanding of modern physics," Leifer says. "Thermodynamics is not the closed-book, 19th century physics that we thought it was."

Explaining how thermodynamics works on the quantum scale is surely a key step in developing the technologies of tomorrow. But it is not just about practical applications—this work can provide insights into the very foundation of modern theory. "Understanding the ultimate limits on how we can manipulate small numbers of quantum systems may help us better understand the laws of quantum physics themselves," says Leifer.