Work

Weak-Memory Dynamics in Discrete Time

Year: 2026

Type: article

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 timescale, 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.

Source: Physical Review Letters

DOI: 10.1103/kdhy-66b6

Authors: Hugues Meyer, Kay Brandner

Institution: University of Nottingham

Language: English

Topic: Advanced Thermodynamics and Statistical Mechanics

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,750

Funders: Medical Research Council, Engineering and Physical Sciences Research Council