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Quantum Fokker-Planck structure of the Lindblad equation

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Mário J. de Oliveira

Statistical Mechanics · Submitted 9 May 2023

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

The authors' main claim We show that the quantum Fokker-Planck equation, obtained by a canonical quantization of its classical version, can be transformed into an equation of the Lindblad form.

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arXiv ID2305.05805 (version 1)
Pith IDLFB3DXMJ, Pith's permanent record of this paper and its review
CitationM\'ario J. de Oliveira. "Quantum Fokker-Planck structure of the Lindblad equation." arXiv:2305.05805 (2023). https://pith.science/paper/LFB3DXMJ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,591 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.07 · mentions code or data availability 0.02.

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

We show that the quantum Fokker-Planck equation, obtained by a canonical quantization of its classical version, can be transformed into an equation of the Lindblad form. This result allows us to conclude that the quantum Fokker-Planck equation preserves the trace and positivity of the density operator. The Fokker-Planck structure gives explicit expression for the quantum equivalence of probability current as well as the quantum equivalence of detailed balance. We also propose expression for the rate of entropy production and show that it does not vanish for a closed system except in equilibrium.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that the quantum Fokker-Planck equation, obtained by a canonical quantization of its classical version, can be transformed into an equation of the Lindblad form. result 0.69 0.93 0.72 asserted 1.00
s1 This result allows us to conclude that the quantum Fokker-Planck equation preserves the trace and positivity of the density operator. interpretation 0.86 0.86 0.36 asserted 0.98
s2 The Fokker-Planck structure gives explicit expression for the quantum equivalence of probability current as well as the quantum equivalence of detailed balance. result 0.86 0.82 0.10 asserted 1.00
s3 We also propose expression for the rate of entropy production and show that it does not vanish for a closed system except in equilibrium. contribution 0.52 0.94 0.11 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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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 show that the quantum Fokker-Planck equation, obtained by a canonical quantization of its classical version, can be transformed into an equation of the Lindblad form. This result allows us to conclude that the quantum Fokker-Planck equation preserves the trace and positivity of the density operator. The Fokker-Planck structure gives explicit expression for the quantum equivalence of probability current as well as the quantum equivalence of detailed balance. We also propose expression for the rate of entropy production and show that it does not vanish for a closed system except in equilibrium.

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