Super Mario's prison break -- a proposal of object-intelligent-feedback-based classical Zeno and anti-Zeno effects

TL;DR

This paper models a scenario inspired by Super Mario where frequent checks prevent escape (Zeno effect) and infrequent checks facilitate escape (anti-Zeno effect), illustrating classical quantum-like effects in a potential well setting.

Contribution

It proposes a novel classical analogy of Zeno and anti-Zeno effects using a game-inspired scenario with feedback-based checks affecting escape probabilities.

Findings

Frequent checks inhibit escape, demonstrating a classical Zeno effect.

Infrequent checks accelerate escape, illustrating a classical anti-Zeno effect.

The model links feedback timing with escape dynamics in a potential well.

Abstract

Super Mario is imprisoned by a demon in a finite potential well. He can escape from the well with the help of a flight of magic stairs floating in the space. However, the hateful demon may occasionally check his status. At that time, he has to make a judgement of either jumping to the inside ground immediately in order to avoid the discovery of his escape intention, or speeding up his escape process. Therefore, if the demon checks him too frequently such that there is no probability for him to reach the top of the barrier, he will be always inside the well, then a classical Zeno effect occurs. On the other hand, if the time interval between two subsequent checks is large enough such that he has a higher probability of being beyond the demon's controllable range already, then the demon's check actually speeds up his escape and a classical anti-Zeno effect takes place.