Entropy production for quantum dynamical semigroups
Abstract
In analogy to the phenomenological theory of irreversible thermodynamics we define the entropy production for an arbitrary quantum dynamical semigroup with a stationary state. We prove that the entropy production is convex and positive and that the entropy production is a measure of dissipativity of the semigroup. The entropy production is used to prove the approach to equilibrium and to classify the stationary states of semigroups arising in the weak coupling limit.
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A global derivation of the master equation that prediagonalizes the total network Hamiltonian is always consistent with the second law of thermodynamics.
“A global derivation of the master equation which prediagonalizes the total network Hamiltonian and within this framework derives the master equation, is always consistent with the second law of thermodynamics.”
From The local approach to quantum transport may violate the second law of thermodynamics (2014) · cites this paper as [19]
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References 8 · Cited by 444
- Authors
- Spohn, H.
- Affiliations
- Princeton University (US)
- Corresponding author
- Spohn, Herbert
- ORCID
- Spohn, Herbert
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1978-05-01
- Volume
- 19
- Issue
- 5
- Pages
- 1227-1230
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2046908285
- Semantic Scholar
- 2a85c5339b600e71e8d7bdecd78679efe3ced9ac
- Cited by
- 444
- References
- 8
- Citations by year
- 2026: 55 · 2025: 29 · 2024: 30 · 2023: 28 · 2022: 35 · 2021: 32 · 2020: 29 · 2019: 30 · 2018: 29 · 2017: 25 · 2016: 16 · 2015: 18 · 2014: 13 · 2013: 9 · 2012: 6
- FWCI
- 5.52
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Mathematical Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- entropy production, quantum dynamical semigroups, stationary states, non-equilibrium thermodynamics, convexity, dissipativity, convergence to equilibrium, weak coupling limit, open quantum systems
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