How chaos theory connects two seemingly different areas of physics

Particle thermometer

One of many particles acts as a “thermometer,” and the complete system is simulated on a pc. Credit score: TU Wien

A brand new examine at TU Wien reveals how chaos principle hyperlinks quantum principle and thermodynamics, two seemingly separate areas of physics.

A single particle doesn’t have a temperature, it solely has a sure power or velocity. A well-defined temperature can solely be derived when many particles with random velocity distributions are current.

The connection between thermodynamics and quantum physics has been the topic of accelerating curiosity in recent times. researchers in TU Wien They used pc simulations to research this relationship, and located that chaos performs an essential position. Simulations point out that the legal guidelines of thermodynamics can solely be derived from quantum physics when chaos is current.

Boltzmann: Something is feasible, however it might even be inconceivable

Air particles flying randomly in a room can assume an unimaginable variety of completely different states: completely different positions and completely different speeds are allowed for every particular person particle. However not all of those states are equally seemingly. says Professor Eva Brezinova of the Institute for Theoretical Physics at TU Wien. “However that is so unlikely that it’ll not be seen in observe.”

The possibilities of various allowable states will be calculated – in accordance with the formulation developed by the Austrian physicist Ludwig Boltzmann in accordance with the principles of classical physics. And from this likelihood distribution the temperature can be learn: it’s decided just for a lot of particles.

The entire world as a single quantum state

Nevertheless, this causes issues when coping with quantum physics. When a lot of quantum particles are in play on the similar time, the equations of quantum principle turn into so advanced that even the most effective supercomputers on the planet don’t have any likelihood of fixing them.

In quantum physics, particular person particles can’t be thought-about independently of one another, as is the case with basic billiard balls. Every billiard ball has its personal particular person path and particular person location at every cut-off date. However, quantum particles should not particular person – they will solely be described collectively, in a single giant quantum wave operate.

“In quantum physics, the complete system is described by one giant multiparticle quantum state,” says Professor Joachim Burgdorfer (TU Wien). “How the random distribution and thus temperature ought to come up from this has lengthy been a thriller.”

Chaos principle as a mediator

A group at TU Wien has now been capable of present that chaos performs a significant position. To do that, the group ran pc simulations of a quantum system made up of a lot of particles — many indistinguishable (“thermal bathtub”) and one in every of a special kind of particle, the “pattern particle” whose thermometer operates. Every particular person quantum wavefunction of a giant system has a particular power, however not a well-defined temperature – similar to a person classical particle. However for those who now select a pattern particle from the only quantum state and measure its velocity, you possibly can surprisingly discover a velocity distribution comparable to a temperature that matches well-established legal guidelines of thermodynamics.

“It will depend on whether or not it’s messy or inappropriate – that is clearly proven by our calculations,” says Iva Brezinova. “We will particularly change the interactions between particles on the pc and thus create both a very chaotic system, or a system that reveals no chaos in any respect — or something in between.” In doing so, one finds that the presence of chaos determines whether or not or not the quantum state of a pattern particle reveals a Boltzmann temperature distribution.

“With out making any assumptions about random distributions or thermodynamic guidelines, thermodynamic conduct arises from quantum principle alone — if the mixed system of pattern particles and the thermal bathtub behaves quantum chaotically. Joachim Burgdorfer explains how such conduct suits the well-known Boltzmann equations and is set by chaos energy.

This is without doubt one of the first instances wherein the interplay of three essential theories has been rigorously demonstrated by pc simulations of many particles: quantum principle, thermodynamics, and chaos principle.

Reference: “Canonical Density Matrices from Eigenstates of Combined Methods” By Mehdi Korebaz, Stefan Donsa, Fabian Lackner, Joachim Burgdorfer, Eva Bezinova, November 29, 2022, Accessible right here. entropy.
DOI: 10.3390/e24121740

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