Signatures of non-Markovianity in classical single-time probability distributions

Abstract

We show that the Kolmogorov distance allows to quantify memory effects in classical stochastic processes by studying the evolution of the single-time probability distribution. We further investigate the relation between the Kolmogorov distance and other sufficient but not necessary signatures of non-Markovianity within the classical setting.

8 pages, 2 figures, to appear in Physica Scripta T: Proceedings of 19th Central European Workshop on Quantum Optics (Romania, May 2012)

References in corpus (6)

• Assessing non-Markovian dynamics
• Continuous quantum measurement and Itô formalism
• On measures of non-Markovianity: divisibility vs. backflow of information
• Quantum Semi-Markov Processes
• Structure of completely positive quantum master equations with memory kernel
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Cited by in corpus (6)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes
• Interaction-induced correlations and non-Markovianity of quantum dynamics
• Transfer-tensor description of memory effects in open-system dynamics and multi-time statistics
• Non-Markovianity, entropy production, and Jarzynski equality
• Phase space measures of information flow in open systems: A quantum and classical perspective of non-Markovianity