## Effects of Chaos Theory on Thermodynamics and Entropy

A single particle does not have a temperature, as it only has a specific energy or speed. It is only when studying the random velocity distributions of many particles that a well-defined temperature can be determined. Researchers at TU Wien have used computer simulations to investigate how the laws of thermodynamics can arise from the laws of quantum physics. They found that chaos is crucial for the emergence of the rules of thermodynamics from quantum physics.

The air molecules randomly moving around in a room can exist in an almost infinite number of different states, with each particle having different locations and speeds. However, not all of these states are equally likely to occur. According to the rules of classical physics, the probabilities of different allowed states can be calculated using a formula developed by the Austrian physicist Ludwig Boltzmann. This probability distribution can then be used to determine the temperature, which is only defined for a large number of particles. Professor Iva Brezinova from the Institute of Theoretical Physics at TU Wien notes that while it is theoretically possible for all the energy in a space to be transferred to a single particle, this is extremely unlikely to happen in practice.

However, this approach becomes problematic when dealing with quantum physics. The equations of quantum theory become too complex to be solved by even the most powerful supercomputers when a large number of quantum particles are involved. In contrast to classical physics, where individual particles can be considered independently of one another, quantum particles cannot be described individually. Instead, they must be described together as part of a single large quantum wave function. This means that their individual properties, such as location and trajectory, cannot be determined.

The fact that it is difficult to determine the individual properties of quantum particles has long posed a challenge for physicists. “In quantum physics, the entire system is described by a single large many-particle quantum state,” explains Professor Joachim Burgdörfer from TU Wien. “For a long time, it was unclear how a random distribution and thus a temperature could emerge from this description.”

A team at TU Wien has discovered that chaos is essential for the emergence of the laws of thermodynamics from quantum physics. The team performed a computer simulation of a quantum system consisting of many indistinguishable particles, known as a “heat bath,” and one different particle, known as the “sample particle,” which acts as a thermometer. While each individual quantum wave function of the large system has a specific energy, it does not have a well-defined temperature, just like a single classical particle. However, when the velocity of the sample particle is measured, it is found to have a velocity distribution that corresponds to a temperature that fits the known laws of thermodynamics. This suggests that chaos plays a crucial role in the emergence of temperature from quantum physics.

According to Iva Brezinova, “Our calculations showed that the presence of chaos determines whether a quantum state of the sample particle displays a Boltzmann temperature distribution or not.” The team was able to control the level of chaos in the system by changing the interactions between the particles in the computer simulation. This allowed them to create a system that was completely chaotic, one that showed no chaos at all, or anything in between. This demonstrated that chaos is essential for the emergence of temperature from quantum physics.

The research team at TU Wien has demonstrated the connection between quantum physics, thermodynamics, and chaos theory through many-particle computer simulations. This is one of the first instances in which the interplay between these three theories has been rigorously demonstrated. The team found that thermodynamic behavior arises from quantum theory on its own if the combined system of the sample particle and heat bath behaves quantum chaotically. The strength of the chaos determines how well this behavior fits the known Boltzmann formulae. The findings were published in the journal Entropy.

Quotation: https://phys.org/news/2022-12-chaos-theory-quantum-thermodynamics.html

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