Measuring disorder in the quantum realm is creating a bit of a mess. A mathematical study found that three different definitions of entropy that were previously thought to be equivalent don鈥檛 always match for quantum objects. This could have far-reaching implications, as it could force a rewrite of well-established models for聽thermodynamics.
When two objects are connected 鈥� say a container of hot gas is linked to a colder gas reservoir 鈥� the entropy of the colder one can increase because the two will exchange quantities like particles and heat. For almost 200 years, physicists have used the same set of equations to calculate just how much entropy is produced in every such process. But they may have been oblivious to quantum complications, says at the National Institute of Standards and Technology in Maryland. She and her colleagues wanted to make them clear.
They focused on the quantum phenomenon of 鈥渘oncommuting quantities鈥�, the idea that the properties of a quantum object, as determined through measurements, can depend on the order in which those measurements are made.
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More conventionally, we think of most quantities as 鈥渃ommuting鈥濃�� if you measure a rectangle鈥檚 length and then its width, you鈥檒l get the same results as when you measure the width before the length. Or take the example of the two connected containers of gas, which are exchanging particles and heat. It doesn鈥檛 matter which property you measure first 鈥� the number of particles or the amount of heat that passed between them 鈥� because these two quantities commute.
But properties like quantum spin are trickier. For instance, a single particle can have several types of spin, such as vertical and horizontal, and these don鈥檛 commute. So, when two objects are exchanging spins, measuring the amount of horizontal spin first and then vertical spin will produce a different value than measuring them in reverse order.
鈥淎 measurement can tell us that the system has some amount of this particular quantity, but it totally messes up the amount of the other quantity,鈥� says Yunger Halpern.
Using such noncommuting measurements to determine changes in a system鈥檚 properties, such as its entropy, is thus more complicated. In fact, when the researchers used three different equations for entropy production 鈥� which give the same answer when used for commuting quantities 鈥� they found that they disagreed for the noncommuting case.
Each equation corresponded to a specific conceptual understanding of entropy; for instance, entropy as a measure of disorder versus entropy as a measure of how hard it would be to reverse the heat exchange process. Their inequivalence may have repercussions for how we understand entropy overall.
鈥淲e kept discussing what would happen if we wrote down a checklist of properties that entropy production should have. And we couldn鈥檛 find a unified definition that would satisfy it,鈥� says at the University of Rochester in New York, who worked on the project.
at Harvard University says that, historically, whenever physicists removed the assumption that quantities must commute, many well-established mathematical models 鈥� for studies of heat, entropy and energy or thermodynamics 鈥� had to be adjusted. 鈥淚t鈥檚 kind of like a Jenga tower: you pull out one block and all the other blocks fall down,鈥� he says.
In his view, it is too early to know whether some more unified definition of entropy production can still be formulated. But he takes the new study as a note of caution for future analyses in the quantum realm. 鈥淏ased on what you鈥檙e studying, you now have to be careful when you鈥檙e picking out the definition. In the more classical case, you don鈥檛 have to worry about that,鈥� says Majidy.
Yunger Halpern鈥檚 team is interested in testing this in practice. They are already collaborating on an experiment with quantum bits, like those used in quantum computers. And they are gearing up for more mathematical work. 鈥淚 think that we need to now go around to absolutely every facet of thermodynamics and ask, what happens here [now]?鈥� she says.
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