Thermodynamic length for far-from-equilibrium quantum systems
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We consider a closed quantum system initially at thermal equilibrium and driven by arbitrary external parameters. We derive a lower bound on the entropy production which we express in terms of the Bures angle between the nonequilibrium and the corresponding equilibrium state of the system. The Bures angle is an angle between mixed quantum states and defines a thermodynamic length valid arbitrarily far from equilibrium. As an illustration, we treat the case of a time-dependent harmonic oscillator for which we obtain analytic expressions for generic driving protocols.
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The Clausius inequality Σ = S(ρτ||ρeqτ) ≥ 0 holds.
“Therefore, Σ can be expressed as a relative entropy, which is always non-negative, and hence we have the Clausius inequality [27,86]”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [86]
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- Authors
- Deffner, S., & Lutz, E.
- Affiliations
- University of Maryland, College Park (US)
- Freie Universität Berlin (DE)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2013-02-28
- Volume
- 87
- Issue
- 2
- Pages
- 022143-022143
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2049047546
- Cited by
- 56
- References
- 49
- Citations by year
- 2026: 5 · 2025: 1 · 2024: 3 · 2022: 7 · 2021: 8 · 2020: 7 · 2019: 3 · 2018: 2 · 2017: 9 · 2016: 3 · 2015: 5 · 2014: 3
- FWCI
- 2.61
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical Review E (publishedVersion, other-oa)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Maryland Shared Open Access Repository (USMAI Consortium) (submittedVersion)
- Refubium (Universitätsbibliothek der Freien Universität Berlin) (submittedVersion)
- arXiv (Cornell University)
- Digital Repository at the University of Maryland (University of Maryland College Park)
- Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver
- Funders
- Deutscher Akademischer Austauschdienst
- Deutsche Forschungsgemeinschaft (LU1382/4-1)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- thermodynamic length, entropy production, nonequilibrium quantum systems, closed quantum systems, time-dependent harmonic oscillator, mixed quantum states
- MeSH terms
- Computer Simulation, Energy Transfer, Models, Chemical, Quantum Theory, Thermodynamics, Models, Statistical
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