Quantum Systems Show Entropy Increase, Aligning with Thermodynamic Laws

Quantum Systems Show Entropy Increase, Aligning with Thermodynamic Laws
by Robert Schreiber
Berlin, Germany (SPX) Jan 30, 2025

The second law of thermodynamics, a cornerstone of physics, posits that systems will move toward greater disorder over time. It asserts that entropy, a measure of this disorder, increases in every closed system. This principle is observed in the everyday world: ordered ice crystals melt into water, porcelain vases shatter, and other structures lose their arrangement. However, when it comes to quantum physics, there seemed to be an anomaly. Mathematically, the entropy of quantum systems appeared to remain constant, raising questions about the compatibility of quantum mechanics with classical thermodynamic principles.

A research team from TU Wien (Vienna University of Technology) has now resolved this apparent contradiction, showing that the behavior of entropy in quantum systems is dependent on the definition of entropy being used. By introducing an entropy measure that aligns with quantum theory, the researchers demonstrated that entropy does indeed increase over time in quantum systems, reaching a state of maximal disorder, just as in classical systems.

Understanding Entropy and Time

The concept of entropy is frequently associated with disorder, but it is more accurately described in terms of statistical probabilities. According to Professor Marcus Huber of the Institute for Atomic and Subatomic Physics at TU Wien, entropy measures the likelihood of a system being in a specific state. "Entropy is a measure of whether a system is in a special, very particular state, in which case the system has low entropy, or whether it is in one of many states that look more or less the same, in which case it has high entropy," explained Huber.

For instance, consider a box containing balls sorted by color. When the box is shaken, the previously ordered system transitions into a disordered state, increasing its entropy. "This is simply due to the fact that only a few ordered states exist, but many that are similarly disordered," Huber added.

Entropy is also central to the concept of time. "From a physical point of view, this is what defines the direction of time," noted Max Lock of TU Wien. "In the past, entropy was lower; the future is where entropy is higher." This description of time, however, faced a complication within quantum mechanics: John von Neumann showed that the entropy of a quantum system, when fully understood, remains unchanged, and thus time's direction becomes indistinguishable from a quantum perspective.

The Quantum Perspective

Quantum mechanics presents unique challenges. According to Tom Rivlin of TU Wien, quantum systems do not allow complete information about their state. Instead, measurements are probabilistic, providing only partial knowledge. "We can choose a property of the system that we want to measure - a so-called observable. This can be, for example, the location of a particle or its speed," explained Rivlin. Even with knowledge of probabilities, the outcome remains uncertain.

This uncertainty must be factored into entropy calculations. Instead of considering the entire quantum system's entropy, which remains static, the team proposed focusing on Shannon entropy. This form of entropy takes into account the probabilities of different outcomes, and its value increases when there are many possible measurement results with similar probabilities. As Florian Meier of TU Wien put it, "Shannon entropy is a measure of how much information you gain from the measurement." When there is only one possible outcome, the entropy is zero, and no new information is gained. However, when many outcomes are likely, the entropy is high.

The Proof: Quantum Disorder Unfolds

By focusing on Shannon entropy, the researchers demonstrated that, just as in classical systems, entropy increases in closed quantum systems over time. The system's entropy grows as the measurement results become increasingly uncertain, reaching a peak that mirrors the disorder found in classical thermodynamics. These findings were supported by mathematical models and confirmed through computer simulations of interacting quantum particles.

"This shows us that the second law of thermodynamics is also true in a quantum system that is completely isolated from its environment," concluded Marcus Huber. "You just have to ask the right questions and use a suitable definition of entropy."

While these findings have less relevance for small quantum systems, such as a single hydrogen atom, they are critical for understanding large quantum systems used in modern technology. "To describe such many-particle systems, it is essential to reconcile quantum theory with thermodynamics," Huber emphasized. "That's why we also want to use our basic research to lay the foundation for new quantum technologies."

Research Report:Emergence of a Second Law of Thermodynamics in Isolated Quantum Systems