Delayed and Predictive Dynamics with Stochastic Time

TL;DR

This paper introduces classical models with stochastic time variables that can induce resonance phenomena, offering a new perspective on stochastic resonance and potential foundations for extended stochastic theories in physics.

Contribution

It presents a novel approach by modeling noise in the time variable alone, contrasting with traditional stochastic dynamics, and explores resonance effects in such models.

Findings

Models can induce stochastic resonance with varying noise levels.

Resonance phenomena differ from traditional stochastic dynamics.

Potential for extending to stochastic space-time theories.

Abstract

We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal description of stochastic dynamics. The notable feature is that these models can induce a "resonance" with varying noise strengths in the time variable. Thus, they provide a different mechanism for ``stochastic resonance'', which has been discussed within the normal context of stochastic dynamics. In a broader context, we expect these simple models and associated behaviours may serve as one of the starting points to construct and investigate an extended classical dynamical theory where both the space and time variables are taken as stochastic. We need to explore if such approaches can be further developed for both classical and quantum applications.