Weak-Memory Dynamics in Discrete Time

Hugues Meyer; Kay Brandner

doi:10.1103/kdhy-66b6

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arXiv · 2510.26325

Weak-Memory Dynamics in Discrete Time

Hugues Meyer·Kay Brandner

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Abstract

Discrete dynamics arise naturally in systems with broken temporal translation symmetry and are typically described by first-order recurrence relations representing classical or quantum Markov chains. When memory effects induced by hidden degrees of freedom are relevant, however, higher-order discrete evolution equations are generally required. Focusing on linear dynamics, we identify a well-delineated weak-memory regime where such equations can, on an intermediate time scale, be systematically reduced to a unique first-order counterpart acting on the same state space. We formulate our results as a mathematical theorem and work out two examples showing how they can be applied to stochastic Floquet dynamics under coarse-grained and quantum collisional models.

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Hugues Meyer, Kay Brandner. 2025-10-30. Weak-Memory Dynamics in Discrete Time. https://doi.org/10.1103/kdhy-66b6

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