Weak-Memory Dynamics in Discrete Time

• URL: http://arxiv.org/abs/2510.26325v1
• Date: Thu, 30 Oct 2025 10:17:37 GMT
• Title: Weak-Memory Dynamics in Discrete Time
• Authors: Hugues Meyer, Kay Brandner,
• Abstract summary: We show how low-delineated weak-memory equations can be systematically reduced to a unique first-order counterpart acting on the same state space.<n>We formulate our results as a mathematical theorem and work out two examples showing how they can be applied to Floquet dynamics under coarse-grained and quantum collisional models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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