Sacred laws of entropy also work in the quantum world, suggests study
According to the second law of thermodynamics, the entropy of an isolated system tends to increase over time. Everything around us follows this law; for instance, the melting of ice, a room becoming messier, hot coffee cooling down, and aging — all are examples of entropy increasing over time.
Until now, scientists believed that quantum physics is an exception to this law. This is because about 90 years ago, mathematician John von Neumann published a series of papers in which he mathematically showed that if we have complete knowledge of a system's quantum state, its entropy remains constant over time.
However, a new study from researchers at the Vienna University of Technology (TU Wien) challenges this notion. It suggests that the entropy of a closed quantum system also increases over time until it reaches its peak level.
'It depends on what kind of entropy you look at. If you define the concept of entropy in a way that is compatible with the basic ideas of quantum physics, then there is no longer any contradiction between quantum physics and thermodynamics,' the TU Wien team notes.
The study authors highlighted an important detail in Neumann's explanation. He stated that entropy for a quantum system doesn't change when we have full information about the system.
However, the quantum theory itself tells us that it's impossible to have complete knowledge of a quantum system, as we can only measure certain properties with uncertainty. This means that von Neumann entropy isn't the correct approach to looking at the randomness and chaos in quantum systems.
https://youtu.be/iWgKxZIA2uA
So then, what's the right way? Well, 'instead of calculating the von Neumann entropy for the complete quantum state of the entire system, you could calculate an entropy for a specific observable,' the study authors explain.
This can be achieved using Shannon entropy, a concept proposed by mathematician Claude Shannon in 1948 in his paper titled A Mathematical Theory of Communication. Shannon entropy measures the uncertainty in the outcome of a specific measurement. It tells us how much new information we gain when observing a quantum system.
"If there is only one possible measurement result that occurs with 100% certainty, then the Shannon entropy is zero. You won't be surprised by the result, you won't learn anything from it. If there are many possible values with similarly large probabilities, then the Shannon entropy is large," Florian Meier, first author of the study and a researcher at TU Wien, said.
When we reimagine the entropy of a quantum system through the lens of Claude Shannon, we begin with a quantum system in a state of low Shannon entropy, meaning that the system's behavior is relatively predictable.
For example, imagine you have an electron, and you decide to measure its spin (which can be up or down). If you already know the spin is 100% up, the Shannon entropy is zero—we learn nothing new from the measurement.
In case the spin is 50% up and 50% down, then Shannon entropy is high because we are equally likely to get either result, and the measurement gives us new information. As more time passes, the entropy increases as you're never sure about the outcome.
However, eventually, the entropy reaches a point where it levels off, meaning the system's unpredictability stabilizes. This mirrors what we observe in classical thermodynamics, where entropy increases until it reaches equilibrium and then stays constant.
According to the study, this case of entropy also stands valid for quantum systems involving many particles and producing multiple outcomes.
"This shows us that the second law of thermodynamics is also true in a quantum system that is completely isolated from its environment. You just have to ask the right questions and use a suitable definition of entropy," Marcus Huber, senior study author and an expert in quantum information science at TU Wien, said.
The study is published in the journal PRX Quantum.
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