How chaos theory connects two seemingly different areas of physics

Particle thermometer

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

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

A single particle doesn’t have a temperature, it solely has a sure vitality 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 necessary 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 unbelievable

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 probably. 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 could be calculated – in keeping with the formulation developed by the Austrian physicist Ludwig Boltzmann in keeping with the foundations of classical physics. And from this chance distribution the temperature may also be learn: it’s decided just for numerous particles.

The entire world as a single quantum state

Nevertheless, this causes issues when coping with quantum physics. When numerous quantum particles are in play on the identical time, the equations of quantum idea grow to be so complicated that even the very best supercomputers on this planet haven’t 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. Alternatively, quantum particles aren’t particular person – they’ll solely be described collectively, in a single massive quantum wave operate.

“In quantum physics, all the system is described by one massive 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 idea as a mediator

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

“It relies 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 totally 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 displays a Boltzmann temperature distribution.

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

This is likely one of the first circumstances during which the interplay of three necessary theories has been rigorously demonstrated by pc simulations of many particles: quantum idea, thermodynamics, and chaos idea.

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

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