Deriving a kinetic uncertainty relation for piecewise deterministic processes: from classical to quantum

TL;DR

This paper derives a kinetic uncertainty relation for Markovian piecewise deterministic processes, extending classical results to quantum systems, with explicit stationary distributions, large deviation rate functionals, and a practical quantum example.

Contribution

It introduces a method to derive a kinetic uncertainty relation for PDPs and extends these classical results to open quantum systems, providing a new theoretical framework.

Findings

Explicit stationary distributions for classical PDPs

Derivation of a rate functional of large deviations

Extension of classical results to quantum systems using a two-level example

Abstract

From the perspective of Markovian piecewise deterministic processes (PDPs), we investigate the derivation of a kinetic uncertainty relation (KUR), which was originally proposed in Markovian open quantum systems. First, stationary distributions of classical PDPs are explicitly constructed. Then, a tilting method is used to derive a rate functional of large deviations. Finally, based on an improved approximation scheme, we recover the KUR. These classical results are directly extended to the open quantum systems. We use a driven two-level quantum system to exemplify the quantum results.