Thermalisation

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In physics, thermalisation (or thermalization) is the process of physical bodies reaching thermal equilibrium through mutual interaction. In general, the natural tendency of a system is towards a state of equipartition of energy and uniform temperature that maximizes the system's entropy. Thermalisation, thermal equilibrium, and temperature are therefore important fundamental concepts within statistical physics, statistical mechanics, and thermodynamics; all of which are a basis for many other specific fields of scientific understanding and engineering application.

Contents

Examples of thermalisation include:

The hypothesis, foundational to most introductory textbooks treating quantum statistical mechanics, [4] assumes that systems go to thermal equilibrium (thermalisation). The process of thermalisation erases local memory of the initial conditions. The eigenstate thermalisation hypothesis is a hypothesis about when quantum states will undergo thermalisation and why.

Not all quantum states undergo thermalisation. Some states have been discovered which do not (see below), and their reasons for not reaching thermal equilibrium are unclear as of March 2019.

Theoretical description

The process of equilibration can be described using the H-theorem or the relaxation theorem, [5] see also entropy production.

Systems resisting thermalisation

Classical systems

Broadly-speaking, classical systems with non-chaotic behavior will not thermalise. Systems with many interacting constituents are generally expected to be chaotic, but this assumption sometimes fails. A notable counter example is the Fermi–Pasta–Ulam–Tsingou problem, which displays unexpected recurrence and will only thermalise over very long time scales. [6] Non-chaotic systems which are pertubed by weak non-linearities will not thermalise for a set of initial conditions, with non-zero volume in the phase space, as stated by the KAM theorem, although the size of this set decreases exponentially with the number of degrees of freedom. [7] Many-body integrable systems, which have an extensive number of conserved quantities, will not thermalise in the usual sense, but will equilibrate according to a generalized Gibbs ensemble. [8] [9]

Quantum systems

Some such phenomena resisting the tendency to thermalize include (see, e.g., a quantum scar): [10]

Other systems that resist thermalisation and are better understood are quantum integrable systems [23] and systems with dynamical symmetries. [24]

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References

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  7. ↑ Dumas, H. Scott (2014). The KAM Story – A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov–Arnold–Moser Theory. [Hackensack], New Jersey: World Scientific Publishing Company Incorporated. ISBN   978-981-4556-58-3.
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  16. 1 2 Luukko, Perttu J. J.; Drury, Byron; Klales, Anna; Kaplan, Lev; Heller, Eric J.; Räsänen, Esa (2016-11-28). "Strong quantum scarring by local impurities". Scientific Reports. 6 (1): 37656. arXiv: 1511.04198 . Bibcode:2016NatSR...637656L. doi:10.1038/srep37656. ISSN   2045-2322. PMC   5124902 . PMID   27892510.
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  19. 1 2 Keski-Rahkonen, Joonas (2020). Quantum Chaos in Disordered Two-Dimensional Nanostructures. Tampere University. ISBN   978-952-03-1699-0.
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  22. ↑ Wei, Ken Xuan; Ramanathan, Chandrasekhar; Cappellaro, Paola (2018). "Exploring Localization in Nuclear Spin Chains". Physical Review Letters. 120 (7): 070501. arXiv: 1612.05249 . Bibcode:2018PhRvL.120g0501W. doi:10.1103/PhysRevLett.120.070501. PMID   29542978. S2CID   4005098.
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