Fifty Years of the GKLS Master Equation: Foundations and Early Developments
Abstract
The year 2026 marks the fiftieth anniversary of the two seminal papers in which Gorini, Kossakowski, and Sudarshan, and independently Lindblad, characterized the generators of completely positive quantum dynamical semigroups. We revisit the conceptual and historical route leading to the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation and examine several of its early developments and consequences. Our aim is to show how several initially separate mathematical and physical ideas converged in the GKLS structure theorem, imme- diately opening the way to manifold consequences for the description of dissipative quantum phenomena and how that theorem, fifty years later, remains both a foundational result and an active framework for open quantum dynamics.
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BibTeX
@misc{benatti2026fifty,
title = {{Fifty Years of the GKLS Master Equation: Foundations and Early Developments}},
author = {Fabio Benatti and Dariusz Chruściński and Saverio Pascazio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19404},
eprint = {2609.19404},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19404},
}
RIS
TY - UNPB
TI - Fifty Years of the GKLS Master Equation: Foundations and Early Developments
AU - Fabio Benatti
AU - Dariusz Chruściński
AU - Saverio Pascazio
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19404
UR - https://arxiv.org/abs/2609.19404
AB - The year 2026 marks the fiftieth anniversary of the two seminal papers in which Gorini, Kossakowski, and Sudarshan, and independently Lindblad, characterized the generators of completely positive quantum dynamical semigroups. We revisit the conceptual and historical route leading to the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation and examine several of its early developments and consequences. Our aim is to show how several initially separate mathematical and physical ideas converged in the GKLS structure theorem, imme- diately opening the way to manifold consequences for the description of dissipative quantum phenomena and how that theorem, fifty years later, remains both a foundational result and an active framework for open quantum dynamics.
ER -