Weak value analogue in classical stochastic process

TL;DR

This paper demonstrates that classical stochastic processes can exhibit quantum-like weak value phenomena, including negative probabilities and abnormal expectations, by formulating their two-time conditional probabilities akin to quantum wave equations.

Contribution

It introduces a novel classical stochastic framework that mimics quantum weak value behaviors, expanding understanding of classical-quantum analogies.

Findings

Negative probabilities observed in a stochastic Ising spin system.

Abnormal expectations exceeding normal bounds in the model.

Classical processes can replicate quantum weak value phenomena.

Abstract

The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the weak value in the quantum mechanics. A negative probability and abnormal expectations of some quantities remarkablely larger than their inherent norms are found in an example of a stochastic Ising spin system.