Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
Open accessAbstract
Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state, we arrive at an additional, independent set of thermodynamic constraints that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilárd engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and the theory of entanglement.
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Translationally invariant quantum operations are a proper subset of incoherent operations.
“Thus, TI quantum operations are a proper subset of incoherent operations (See Fig. 1).”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
The states |0〉+|1〉 and |0〉+|N〉 (N>1) are equivalent resources under Baumgratz et al. coherence theory, so any measure of coherence takes the same value on them.
“From the point of view of the resource theory of coherence proposed by Baumgratz et. al. [25], these states are equivalent resources, because they can be interconverted to each other by incoherent operations of the form (2.7), and therefore any measure of coherence takes the same value on them.”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
For any given observable H, all translationally invariant operations are incoherent operations in the sense of Baumgratz et al. relative to the eigenspaces of H.
“Proposition 2 For any given observable H (in particular, the Hamiltonian), all TI operations are incoherent operations (in the sense defined by Baumgratz et al. [25], relative to the eigenspaces of H ).”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
The Wigner-Yanase skew information is not a measure of coherence according to the definition of Baumgratz et al., because it can increase under incoherent operations.
“However, the latter claim is incorrect.”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
The relative entropy of coherence of Baumgratz et al. has been studied as a measure of asymmetry under the names G-asymmetry and relative entropy of asymmetry, and generalized to Holevo asymmetry measures.
“the function called relative entropy of coherence by Baumgratz et. al. [25] has been extensively studied as a measure of asymmetry under the names of G-asymmetry and relative entropy of asymmetry [29, 32, 39, 41], and it has been generalized to a family of measures of asymmetry, called Holevo asymmetry measures [21, 26]”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
Measures of coherence in the sense of Baumgratz et al. cannot capture any information about the speed of evolution, while any natural notion of speed of evolution is automatically a measure of asymmetry.
“while measures of coherence (in the sense of [25]) cannot capture any information about the speed of evolution, any natural notion of speed of evolution is automatically a measure of asymmetry”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
There exist measures of translational asymmetry that are not measures of coherence in the sense of Baumgratz et al., i.e., they can increase under incoherent operations.
“there are measures of translational asymmetry which are not measures of coherence in the sense of Baumgratz et al., i.e., they can increase under incoherent operations.”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
The speed of evolution can increase unboundedly under incoherent operations, so the notion of coherence studied by Baumgratz et al. does not characterize the speed of evolution.
“Note that the speed of evolution can, however, increase (unboundedly) under what Ref. [25] termed incoherent operations , and so the notion of coherence studied by Baumgratz et. al. [25] does not characterize the speed of evolution.”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
Any measure of coherence in the sense of Baumgratz et al. is also a measure of translational asymmetry.
“Therefore, any measure of coherence in the sense of Baumgratz et al. [25], i.e., a function that is non-increasing under incoherent operations, is also a measure of translational asymmetry.”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
Measures of coherence in the sense of Baumgratz et al. are a proper subset of measures of asymmetry.
“measures of coherence are a proper subset of measures of asymmetry.”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
In the Baumgratz et al. approach, the eigenvalues of the observable defining the preferred basis are irrelevant.
“unlike the first approach based on the notion of asymmetry, in the approach of Baumgratz et. al. [25] the eigenvalues of the observable which defines the preferred basis relative to which coherence is defined are irrelevant.”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
The Wigner-Yanase skew information is a measure of asymmetry which is not a measure of coherence based on the definition of Baumgratz et al.
“In particular, the Wigner-Yanase skew information is a measure of asymmetry which is not a measure of coherence based on the definition of Baumgratz et. al. [25].”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
E_TI is an incoherent operation in the sense of Baumgratz et al.
“it is straightforward to show that E TI is an incoherent operation in the sense of Baumgratz et. al. [25]”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
Measures of coherence in the sense defined by Baumgratz et al. are a proper subset of measures of asymmetry.
“We also showed that measures of coherence in the sense defined by Baumgratz et. al. [25], are a proper subset of measures of asymmetry.”
From Quantum speed limits, coherence, and asymmetry (2016) · cites this paper as [25]
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Self-citation
- Authors
- Lostaglio, M., Jennings, D., & Rudolph, T.
- Affiliations
- Imperial College London (GB)
- Corresponding author
- Lostaglio, Matteo
- Venue
- Nature Communications
- Published
- 2015-03-10
- Volume
- 6
- Issue
- 1
- Pages
- 6383-6383
- ISSN
- 2041-1723 (ISSN-L)
- PMC
- PMC4366492
- OpenAlex
- W2059846772
- Cited by
- 727
- References
- 73
- Citations by year
- 2026: 42 · 2025: 55 · 2024: 59 · 2023: 55 · 2022: 62 · 2021: 59 · 2020: 55 · 2019: 83 · 2018: 89 · 2017: 80 · 2016: 56 · 2015: 32
- FWCI
- 53.94
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Nature Communications (publishedVersion, cc-by)
- arXiv (Cornell University) (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- White Rose Research Online (University of Leeds, The University of Sheffield, University of York) (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- Funders
- Leverhulme Trust
- Royal Society
- Engineering and Physical Sciences Research Council (MP1209, 1229180)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum coherence, nanoscale thermodynamics, time asymmetry, Szilard engine, thermodynamic work, irreversibility, entanglement, thermodynamic constraints
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