Entropy is often crudely described as a measure the "disorder" of a system. But there are different mathematical definitions of entropy that are applied in different realms, for instance in thermodynamics, computing and information, or when describing black holes. Things might be complicated even further when quantum effects come into play.
In a new paper in the journal Physical Review X FQxI quantum theorist Nicole Yunger Halpern, of the University of Maryland, College Park, and colleagues have analysed entropy when defined as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. They have then extended the concept of entropy production to the deeply quantum regime, noting that a crucial quantum effect–the idea that certain operations in the quantum realm do not compute (for instance, it makes a difference whether you choose to first measure an object's position then its momentum or vice versa)–may have an important impact. Their work has now been featured in New Scientist (subscription required).
Yunger Halpern also spoke to Zeeya Merali about this project and its implications for understanding the nature of time in quantum systems, potentially making it easier to build quantum computers, for Templeton Ideas earlier this year. From "Can We Turn Back Time?" in Templeton Ideas:
In the quantum world, whether or not two operations commute has especially profound consequences. When the operations of measuring two quantities, such as momentum and position, do not commute, then the quantities cannot both be measured simultaneously. This is the root of Heisenberg’s uncertainty principle and why we cannot know both the momentum and position of a quantum particle precisely. “Quantum theory is fascinating because…non-commutation leads to measurement disturbance and uncertainty relations,” says Yunger Halpern.
So Yunger Halpern and Kalev analyzed what happens if you take the possibility of non-commutation into account when considering thermalization and found that the textbook predictions need to be tweaked. The system “in some cases and in some senses, doesn’t quite thermalize as much as usual,” says Yunger Halpern.
You can also hear Yunger Halpern speaking about her recent book, Quantum Steampunk on the FQxI Podcast. Her book can be purchased from the FQxI Bookshop. (If you make a purchase through this link, FQxI will receive a donation.)