Generalized Clausius inequality for nonequilibrium quantum processes
Open accessAbstract
We show that the nonequilibrium entropy production for a driven quantum system is larger than the Bures length, the geometric distance between its actual state and the corresponding equilibrium state. This universal lower bound generalizes the Clausius inequality to arbitrary nonequilibrium processes beyond linear response. We further derive a fundamental upper bound for the quantum entropy production rate and discuss its connection to the Bremermann-Bekenstein bound.
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The maximum bound gives the highest rate of quantum entropy production.
“the maximal rate of quantum entropy production [27]”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [27]
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 [27]
The Bremermann-Bekenstein bound was rediscovered in quantum thermodynamics.
“More recently, the Bremerman-Bekenstein bound was re-discovered in quantum thermodynamics [27].”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [27]
A tighter entropy-production bound is Σ ≥ (8/π^2) L^2(ρτ, ρeqτ).
“A tighter bound can be derived by considering the geometric distance between these states [27] Σ 8 π 2 L 2 (ρ τ , ρ eq τ ).(42)”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [27]
The Morozova, Čencov, and Petz theorem provides a one-to-one correspondence between contractive Riemannian metrics and MC functions in finite dimensions.
“The Morozova, Čencov, and Petz theorem provides us with a characterization of such metrics in the finite-dimensional case, by constructing a one-to-one correspondence between them and the Morozova-Čencov (MC) functions”
From Generalized Geometric Quantum Speed Limits (2016) · cites this paper as [51]
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- Authors
- Deffner, S., & Lutz, E.
- Affiliations
- University of Augsburg (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-10-19
- Volume
- 105
- Issue
- 17
- Pages
- 170402-170402
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1994671075
- Cited by
- 245
- References
- 33
- Citations by year
- 2026: 11 · 2025: 21 · 2024: 17 · 2023: 18 · 2022: 18 · 2021: 22 · 2020: 22 · 2019: 25 · 2018: 20 · 2017: 19 · 2016: 17 · 2015: 9 · 2014: 12 · 2013: 8 · 2012: 3
- FWCI
- 3.18
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Physical Review Letters (publishedVersion, other-oa)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Maryland Shared Open Access Repository (USMAI Consortium) (submittedVersion)
- arXiv (Cornell University)
- Digital Repository at the University of Maryland (University of Maryland College Park)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Engineering › Mechanical Engineering › Advanced Thermodynamic Systems and Engines
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- Clausius inequality, Bures distance, geometric entropy, driven quantum systems, non-equilibrium thermodynamics
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