# Frontiers of open quantum system dynamics

## TL;DR

This paper reviews recent advances in open quantum system theory, focusing on formalizing quantum memory effects and non-Markovian dynamics, and comparing them with classical stochastic processes.

## Contribution

It introduces a formalization of non-Markovian quantum dynamics and explores quantum evolution equations with memory kernels, highlighting differences from classical memory concepts.

## Key findings

- Formalization of non-Markovian quantum dynamics
- Construction of quantum evolution equations with memory kernels
- Comparison between quantum and classical memory effects

## Abstract

We briefly examine recent developments in the field of open quantum system theory, devoted to the introduction of a satisfactory notion of memory for a quantum dynamics. In particular, we will consider a possible formalization of the notion of non-Markovian dynamics, as well as the construction of quantum evolution equations featuring a memory kernel. Connections will be drawn to the corresponding notions in the framework of classical stochastic processes, thus pointing to the key differences between a quantum and classical formalization of the notion of memory effects.