On the emergence of classical stochasticity

TL;DR

This paper investigates how classical stochastic behavior emerges from quantum systems described by Pauli-type master equations, highlighting the importance of classical assumptions in calculating stochastic times and illustrating the process with particle examples.

Contribution

It clarifies the logical structure behind the emergence of classical stochasticity from quantum mechanics and emphasizes the role of classical assumptions in stochastic calculations.

Findings

Classical stochasticity depends on classical assumptions about definite states.

Emergence of stochasticity illustrated with particles, bosons, and fermions.

Ultradecoherence limit facilitates the transition from quantum to classical behavior.

Abstract

We examine the logical structure of the emergence of classical stochasticity for a quantum system governed by a Pauli-type master equation. It is well-known that while such equations describe the evolution of probabilities, they do not automatically justify classical reasoning based on the assumption that the system exists in a definite state at intermediate times. On the other hand, we show that this assumption is crucial for the standard calculation of stochastic times such as the persistent time and the time of first arrivals. We then consider examples of single particles, bosons, and fermions in the so-called ultradecoherence limit to illustrate how classical stochasticity may emerge from quantum mechanics.