Weak-Memory Dynamics in Discrete Time
arXiv:2510.26325 · doi:10.1103/kdhy-66b6
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.
References in corpus (62)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Atomic quantum gases in periodically driven optical lattices
- Floquet Engineering of Quantum Materials
- Open Quantum Systems. An Introduction
- Operator Spreading in Random Unitary Circuits
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Fundamental aspects of steady-state conversion of heat to work at the nanoscale
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Floquet scattering theory of quantum pumps
- Stochastic thermodynamics under coarse-graining
- Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
- Solution of a minimal model for many-body quantum chaos
- Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
- Quantum collision models: open system dynamics from repeated interactions
- Universal Lindblad equation for open quantum systems
- Entanglement spreading in a minimal model of maximal many-body quantum chaos
- Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited
- Sub-ballistic growth of Rényi entropies due to diffusion
- Irreversibility, heat and information flows induced by non-reciprocal interactions
- Iterative Reconstruction of Memory Kernels
- Accuracy Assessment of Perturbative Master Equations -- Embracing Non-Positivity
- Thermodynamics of weakly coherent collisional models
- Directed flow in non-adiabatic stochastic pumps
- Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
- Non-Markovianity and negative entropy production rates
- Floquet States in Open Quantum Systems
- Collisional quantum thermometry
- Completely positive master equation for arbitrary driving and small level spacing
- The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets
- Molecular hydrodynamics from memory kernels
- Coarse-Grained Modelling Out of Equilibrium
- Repeated interactions and quantum stochastic thermodynamics at strong coupling
- The Accuracy of Perturbative Master Equations
- Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
- Emergent memory and kinetic hysteresis in strongly driven networks
- Thermodynamically Consistent Coarse Graining of Biocatalysts beyond Michaelis--Menten
- Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
- Coarse graining of master equations with fast and slow states
- Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
- Likelihood-based non-Markovian models from molecular dynamics
- Emergence of molecular friction in liquids: bridging between the atomistic and hydrodynamic pictures
- Is there a Floquet Lindbladian?
- Mimicking Nonequilibrium Steady States with Stochastic Pumps
- Shortcuts to Adiabatic Pumping in Classical Stochastic Systems
- Projection operators in statistical mechanics: a pedagogical approach
- Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
- Manifestations of Projection-Induced Memory: General Theory and the Tilted Single File
- Coarse-grained entropy production with multiple reservoirs: unraveling the role of time-scales and detailed balance in biology-inspired systems
- Violation of Local Detailed Balance Despite a Clear Time-Scale Separation
- Exact quench dynamics of the Floquet quantum East model at the deterministic point
- A Toolbox for Quantifying Memory in Dynamics Along Reaction Coordinates
- Coarse graining of biochemical systems described by discrete stochastic dynamics
- Stochastic thermodynamics of periodically driven systems: Fluctuation theorem for currents and unification of two classes
- Accurate Memory Kernel Extraction from Discretized Time Series Data
- Limit cycles in periodically driven open quantum systems
- Model-free inference of memory in conformational dynamics of a multi-domain protein
- On the emergence of memory in equilibrium versus non-equilibrium systems
- Dynamics of Micro and Nanoscale Systems in the Weak-Memory Regime
- Dynamics of micro and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation
- Strong Markov dissipation in driven-dissipative quantum systems