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  • Open Access

Emergence of classical stochasticity

Xuan Du Trinh*

Ismaël Septembre† and Hai-Chau Nguyen‡

  • Naturwissenschaftlich–Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany

  • *Contact author: xtrinh@cs.stonybrook.edu
  • †Contact author: ismael.septembre@uni-siegen.de
  • ‡Contact author: chau.nguyen@uni-siegen.de
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Phys. Rev. A 114, 042207 – Published 13 October, 2026

DOI: https://doi.org/10.1103/855f-2529

Abstract

We examine 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 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. It is also curious to point out that the standard derivation of the Pauli master equation based on the Fermi Golden Rule actually proceeds by assuming that the system remains in a definite state as the starting point to derive the transition rate to a different state. By studying the so-called ultradecoherence limit, we show that the Pauli master equation can also be arrived at without such an assumption. Instead, that the system exists in a definite state has to be justified by a different argument. We then consider examples of single particles, bosons, and fermions in the ultradecoherence limit to illustrate how classical stochasticity may emerge from quantum mechanics.

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Outline

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Phys. Rev. A 114, 042207– Published 13 October, 2026
  • Received 11 February 2026
  • Revised 23 September 2026
  • Accepted 25 September 2026
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