New quantum study could heat up thermodynamic research

5 Mar 2021

Image: © James Thew/

A new quantum version of a classic thought experiment could pave the way for quantum heat engines.

Researchers have developed a new quantum theory that could pave the way for the development of quantum heat engines.

Mathematicians and physicists from the University of Nottingham have applied this new theory to the so-called Gibbs Paradox, which involves the contrast between mixing two quantities of ideal gases of a different kind and mixing two quantities of the same gas. In the case of different gases, mixing is accompanied by an entropy increase, while in the case of same gases there is no entropy change.

This paradox led to crucial insights for the development of early thermodynamics and emphasises the need to consider an experimenter’s degree of control over a system. Thermodynamics looks at how energy is exchanged between bodies at different temperatures and can help predict the likeliness of certain chemical reactions.

In this latest research, published in Nature Communications, the team developed a theory based on mixing two quantum gases – for example, one red and one blue, otherwise identical – which start separated and then mix in a box.

Overall, the system becomes more uniform, which is quantified by an increase in entropy. If the observer then puts on purple-tinted glasses and repeats the process, the gases look the same so it appears as if nothing changes. In this case, the entropy change is zero.

Benjamin Yadin and Benjamin Morris, lead authors on the research, said: “In order to resolve the paradox, we must realise that thermodynamics tells us what useful things can be done by an experimenter who has devices with specific capabilities.”

To extract useful energy from the mixing process, scientists need devices that can ‘see’ the differences between the gases, which are indistinguishable to the naked eye. The research shows that in the quantum case, despite being unable to tell the difference between the gases, the so-called ‘ignorant’ experimenter can still extract useful energy through mixing them.

At a larger scale, this research suggests that scientists who are able to control these gases with a large quantum device could pave the way for new quantum heat engines.

Prof Gerardo Adesso from the research team added that there are many unknown aspects at the heart of quantum mechanics. “Such a fundamental ignorance, however, doesn’t prevent us from putting quantum features to good use, as our work reveals,” he said.

“We hope our theoretical study can inspire exciting developments in the burgeoning field of quantum thermodynamics and catalyse further progress in the ongoing race for quantum-enhanced technologies.”

Jenny Darmody is the editor of Silicon Republic