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Generalized master equations leading to completely positive dynamics

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Bassano Vacchini

Quantum Physics · Submitted 3 Nov 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions.

how it is stated · asserted 1.00 read the record →

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arXiv ID1611.01150 (version 1)
Pith IDMBMY2N4R, Pith's permanent record of this paper and its review
CitationBassano Vacchini. "Generalized master equations leading to completely positive dynamics." arXiv:1611.01150 (2016). https://pith.science/paper/MBMY2N4R
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,699 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.52 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.78 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes, and puts into evidence the non uniqueness of the relationship arising due to the typical quantum issue of operator ordering. The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory description of the dynamics. Previous apparently unrelated results are now connected in a unified framework, which further allows to phenomenologically construct a large class of non-Markovian evolutions taking as starting point collections of time dependent maps and instantaneous transformations describing the microscopic interaction dynamics.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. contribution 1.00 0.95 0.85 asserted 1.00
s1 The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes, and puts into evidence the non uniqueness of the relationship arising due to the typical quantum issue of operator ordering. method 0.73 0.85 0.09 asserted 1.00
s2 The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory description of the dynamics. interpretation 0.96 0.87 0.10 asserted 0.98
s3 Previous apparently unrelated results are now connected in a unified framework, which further allows to phenomenologically construct a large class of non-Markovian evolutions taking as starting point collections of time dependent maps and instantaneous transformations describing the microscopic interaction dynamics. contribution 0.84 0.82 0.20 asserted 0.96

What kind of paper the classifier reports this is: method or tool 0.52 · evidence from proof or derivation 0.98.

What was examined, and what was not

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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes, and puts into evidence the non uniqueness of the relationship arising due to the typical quantum issue of operator ordering. The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory description of the dynamics. Previous apparently unrelated results are now connected in a unified framework, which further allows to phenomenologically construct a large class of non-Markovian evolutions taking as starting point collections of time dependent maps and instantaneous transformations describing the microscopic interaction dynamics.

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Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper
  • We introduce a general construction of master equations with memory kernel whose solutions are given by completely positive trace preserving maps.

    Quantum renewal processes · 0.85

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