Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Markov approximation revisited: Inconsistency of the standard quantum Brownian motion model

Rocco, A, Grigolini, P

Published Jan 1, 1999• 2 citations
OpenAlex

Abstract

We revisit the Markov approximation necessary to derive ordinary Brownian motion from a model widely adopted in literature for this specific purpose. We show that this leads to internal inconsistencies, thereby implying that further search for a more satisfactory model is required.

Related papers

The Markov approximation revisited: Inconsistency of the standard quantum Brownian motion model

Andrea Rocco, Paolo Grigolini

arXiv:quant-ph/9909051•Physics Letters A•Feb 1, 1999•4 citations

Quantum Brownian Motion Revisited

Aniello Lampo, Miguel Ángel García March, Maciej Lewenstein

SpringerBriefs in physics•Jan 1, 2019•18 citations

Non-Markovian convolutionless master equations from quantum trajectories: Quantum Brownian Motion revisited

Walter T. Strunz, Ting Yu

APS•May 1, 2002•0 citations

Quantum theory of dissipative processes: The Markov approximation revisited

A. J. van Wonderen, K. Lendi

Journal of Statistical Physics•Jul 1, 1995•16 citations

Can quantum Brownian motion be Markovian?

Hermann Grabert

Chemical Physics•Sep 29, 2005•27 citations

The Markovianity of Time: The Category Mistake in Open Quantum Systems

Paul L. Borrill

The Markov approximation is arguably the most ubiquitous tool in physics, underpinning quantum master equations, stochastic processes, and -- via Shannon's channel model and Lamport's logical clocks -- the foundational assumptions of distributed computing. It is widely assumed that Markovianity inherently implies temporal asymmetry: that the Markov property is a forward-in-time-only (FITO) construct. We show that this assumption is a category mistake in the sense of Ryle (1949). Guff, Shastry, and Rocco (2025) have recently demonstrated that the Markov approximation applied to the Caldeira-Leggett model -- a paradigmatic open quantum system -- maintains time-reversal symmetry in the derived equations of motion. The resulting time-symmetric formulations of quantum Brownian motion, Lindblad master equations, and Pauli master equations describe thermalisation that can occur in two opposing temporal directions. Asymmetry arises not from the dynamics but from boundary conditions. We trace how Markovianity's assumed directionality propagated from physics through Shannon's information theory to Lamport's happens-before relation and the impossibility theorems of distributed computing (FLP, CAP, Two Generals). Each step encodes FITO as convention, then treats it as physical law -- the same category mistake repeated across domains. The Surrey result establishes that this conflation is not merely philosophically suspect but mathematically unnecessary: the most fundamental approximation used to derive irreversibility is itself time-symmetric.

arXiv:2603.13738•Mar 14, 2026•0 citations
The Markov approximation is arguably the most ubiquitous tool in physics, underpinning quantum master equations, stochastic processes, and -- via Shannon's channel model and Lamport's logical clocks -- the foundational assumptions of distributed computing. It is widely assumed that Markovianity inherently implies temporal asymmetry: that the Markov property is a forward-in-time-only (FITO) construct. We show that this assumption is a category mistake in the sense of Ryle (1949). Guff, Shastry, and Rocco (2025) have recently demonstrated that the Markov approximation applied to the Caldeira-Leggett model -- a paradigmatic open quantum system -- maintains time-reversal symmetry in the derived equations of motion. The resulting time-symmetric formulations of quantum Brownian motion, Lindblad master equations, and Pauli master equations describe thermalisation that can occur in two opposing temporal directions. Asymmetry arises not from the dynamics but from boundary conditions. We trace how Markovianity's assumed directionality propagated from physics through Shannon's information theory to Lamport's happens-before relation and the impossibility theorems of distributed computing (FLP, CAP, Two Generals). Each step encodes FITO as convention, then treats it as physical law -- the same category mistake repeated across domains. The Surrey result establishes that this conflation is not merely philosophically suspect but mathematically unnecessary: the most fundamental approximation used to derive irreversibility is itself time-symmetric.