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In physics, thermalization (in Commonwealth English "thermalisation") 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. Thermalization, 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.

Examples of thermalization include:

  • the achievement of equilibrium in a plasma.[1]
  • the process undergone by high-energy neutrons as they lose energy by collision with a moderator.[2]

The hypothesis, foundational to most introductory textbooks treating quantum statistical mechanics,[3] assumes that systems go to thermal equilibrium (thermalization). The process of thermalization erases local memory of the initial conditions. The eigenstate thermalization hypothesis is a hypothesis about when quantum states will undergo thermalization and why.

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

Theoretical Description[edit]

The process of equilibration can be described using the H-theorem or the relaxation theorem[4], see also entropy production.

Systems resisting thermalization[edit]

An active research area in quantum physics is systems that resist thermalization.[5] Some such systems include:

  • Quantum scars,[6][7] quantum states with likelihoods of undergoing classical periodic orbits much higher than one would intuitively predict from quantum mechanics[8]
  • Many body localization (MLB),[9] quantum many-body systems retaining memory of their initial condition in local observables for arbitrary amounts of time.[10][11]

As of March 2019, the mechanism for neither of these phenomena is known.[5]


  1. ^ "Collisions and Thermalization". Retrieved 2018-05-14.
  2. ^ "NRC: Glossary -- Thermalization". Retrieved 2018-05-14.
  3. ^ Sakurai JJ. 1985. Modern Quantum Mechanics. Menlo Park, CA: Benjamin/Cummings
  4. ^ Reid, James C.; Evans, Denis J.; Searles, Debra J. (2012-01-11). "Communication: Beyond Boltzmann's H-theorem: Demonstration of the relaxation theorem for a non-monotonic approach to equilibrium". The Journal of Chemical Physics. 136 (2): 021101. doi:10.1063/1.3675847. ISSN 0021-9606.
  5. ^ a b "Quantum Scarring Appears to Defy Universe's Push for Disorder". Quanta Magazine. March 20, 2019. Retrieved March 24, 2019.
  6. ^ Turner, C. J.; Michailidis, A. A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (October 22, 2018). "Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations". Physical Review B. 98 (15): 155134. arXiv:1806.10933. Bibcode:2018PhRvB..98o5134T. doi:10.1103/PhysRevB.98.155134.
  7. ^ Moudgalya, Sanjay; Regnault, Nicolas; Bernevig, B. Andrei (2018-12-27). "Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH". Physical Review B. 98 (23): 235156. arXiv:1806.09624. doi:10.1103/PhysRevB.98.235156. ISSN 2469-9950.
  8. ^ Khemani, Vedika; Laumann, Chris R.; Chandran, Anushya (2019). "Signatures of integrability in the dynamics of Rydberg-blockaded chains". Physical Review B. 99 (16): 161101. arXiv:1807.02108. doi:10.1103/PhysRevB.99.161101.
  9. ^ Nandkishore, Rahul; Huse, David A.; Abanin, D. A.; Serbyn, M.; Papić, Z. (2015). "Many-Body Localization and Thermalization in Quantum Statistical Mechanics". Annual Review of Condensed Matter Physics. 6: 15–38. arXiv:1404.0686. Bibcode:2015ARCMP...6...15N. doi:10.1146/annurev-conmatphys-031214-014726.
  10. ^ Choi, J.-y.; Hild, S.; Zeiher, J.; Schauss, P.; Rubio-Abadal, A.; Yefsah, T.; Khemani, V.; Huse, D. A.; Bloch, I.; Gross, C. (2016). "Exploring the many-body localization transition in two dimensions". Science. 352 (6293): 1547–1552. arXiv:1604.04178. Bibcode:2016Sci...352.1547C. doi:10.1126/science.aaf8834. PMID 27339981.
  11. ^ 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.