# Microscopic modelling of general time-dependent quantum Markov processes

## TL;DR

This paper demonstrates that any CP-divisible quantum process described by a time-local master equation with positive rates can be microscopically modeled, enhancing understanding of open quantum system dynamics.

## Contribution

It provides a microscopic model for all CP-divisible quantum processes governed by time-local master equations with positive rates.

## Key findings

- Any CP-divisible process admits a microscopic model.
- Time-local master equations with positive rates are physically realizable.
- The approach bridges phenomenological equations and microscopic descriptions.

## Abstract

Master equations are typically adopted to describe the dynamics of open quantum systems. Such equations are either in integro-differential or in time-local form, with the latter class more frequently adopted due to the simpler numerical methods developed to obtain the corresponding solution. Here we show that any time-local master equation with positive rates in the generator, i.e. any CP-divisible quantum process, admits a microscopic model whose reduced dynamics is well described by the given equation.