The universe is becoming increasingly disordered as entropy rises, which is a fundamental concept in the second law of thermodynamics. Contrarily, quantum theory suggests that entropy should remain constant. However, scientists have closely examined this seeming discrepancy and clarified it.
One of the key principles of nature is the second law of thermodynamics, which asserts that disorder in the world increases when randomness plays a role. More specifically, it states that entropy must rise within any closed system. As time passes, organized structures lose their arrangement; for instance, ice crystals melt into water, and porcelain vases shatter into fragments. However, at first glance, quantum physics seems to contradict this principle, as mathematical analyses indicate that entropy in quantum systems remains unchanged.
A research group at TU Wien has examined this paradox in detail and demonstrated that the type of entropy you examine affects the outcome. If you define entropy in a way that aligns with quantum physics principles, a contradiction between quantum mechanics and thermodynamics disappears. Ordered quantum systems also experience an increase in entropy until they reach a state of maximum disorder.
Entropy and the Nature of Time
It’s not entirely accurate to equate ‘entropy’ with ‘disorder’. The perception of disorder can be subjective, whereas entropy can be precisely defined through mathematical equations.
“Entropy measures whether a system is in a highly specific state, indicating low entropy, or in one of many similar states, which signifies high entropy,” explains Prof. Marcus Huber from TU Wien’s Institute for Atomic and Subatomic Physics. For example, consider a box filled with balls sorted by color. If you shake the box lightly, over time, a higher-entropy mixed state will emerge due to the limited number of ordered states compared to the many similar disordered states.
“This concept also determines the direction of time,” states Max Lock (TU Wien). “Entropy was lower in the past; the future sees higher entropy.” However, a challenge arises in quantum physics: the mathematician and physicist John von Neumann demonstrated that, according to quantum laws, entropy within a quantum system remains constant. If all information about a quantum system is known, the so-called ‘von Neumann entropy’ does not change; hence, distinguishing the direction of time becomes impossible as each moment is equally valid.
The Limitations of Information
“This perspective overlooks a crucial aspect,” notes Tom Rivlin (TU Wien). “In quantum physics, full information about a system is unattainable. We select a property to measure—referred to as an observable—which might be the location of a particle or its velocity. Quantum theory guides us in understanding the probabilities of various measurement outcomes. However, complete knowledge about the system can never be achieved.”
Even when we understand the probabilities, the actual outcome of any specific measurement remains unpredictable. This element of unpredictability must be factored into the entropy definition. Instead of calculating the von Neumann entropy for the entire quantum state, one could determine an entropy for a specific observable. While the former stays unchanged over time, the latter may fluctuate.
This alternative entropy is known as ‘Shannon entropy’, which is influenced by the probabilities of measuring different values. “Shannon entropy can be seen as a measure of the information gained from a measurement,” explains Florian Meier (TU Wien). “If only one event can occur with absolute certainty, then Shannon entropy equals zero, yielding no surprises or knowledge. Conversely, if multiple results are possible with high probabilities, Shannon entropy is substantial.”
Increasing Quantum Disorder
The research team has demonstrated that starting with a state of low Shannon entropy results in this entropy rising within a closed quantum system until it stabilizes at a maximum value—mirroring the behaviors defined by classical thermodynamic systems. As time progresses, measurement results become less clear, leading to an increased element of surprise during observations. This finding has been mathematically confirmed and corroborated through computer simulations involving several interacting particles.
“This indicates that the second law of thermodynamics holds true in a quantum system totally isolated from its environment. It’s just a matter of asking the right questions and applying an appropriate definition of entropy,” asserts Marcus Huber.
In systems with very few particles, like a hydrogen atom with only a handful of electrons, such analyses might not be pertinent. However, modern technological advances in quantum physics often require the study of systems with numerous particles. “To accurately describe these many-particle systems, it’s crucial to align quantum theory with thermodynamics,” states Marcus Huber. “This is why we aim to use our foundational research to pave the way for new quantum technologies.”
