# An All-Or-Nothing Flavor to the Church-Turing Hypothesis

## TL;DR

This paper explores the physical limits of computation inspired by quantum physics and thermodynamics, suggesting that beyond-Turing computations are either impossible or realizable by simple physical systems.

## Contribution

It introduces an intrinsic physical randomness notion based on thermodynamics and Bell correlations, challenging the universality of the Church-Turing hypothesis.

## Key findings

- Beyond-Turing computations are physically impossible or trivial.
- Bell correlations combined with complexity imply limits on computational power.
- Physical randomness relates to the second law of thermodynamics.

## Abstract

Landauer's principle claims that "Information is Physical." It is not surprising that its conceptual antithesis, Wheeler's "It from Bit," has been more popular among computer scientists --- in the form of the Church-Turing hypothesis: All natural processes can be computed by a universal Turing machine; physical laws then become descriptions of subsets of observable, as opposed to merely possible, computations. Switching back and forth between the two traditional styles of thought, motivated by quantum-physical Bell correlations and the doubts they raise about fundamental space-time causality, we look for an intrinsic, physical randomness notion and find one around the second law of thermodynamics. Bell correlations combined with complexity as randomness tell us that beyond-Turing computations are either physically impossible, or they can be carried out by "devices" as simple as individual photons.