A Thermodynamically Universal Turing Machine

TL;DR

This paper introduces the concept of a thermodynamically universal Turing machine (TUTM) that can simulate any Turing machine's behavior and heat production, linking computation with physical thermodynamics.

Contribution

It formally demonstrates the existence of a TUTM that can replicate both computational and thermodynamic aspects of any Turing machine, extending universality to physical properties.

Findings

TUTM can simulate any Turing machine's input-output behavior.

TUTM can replicate heat production up to an additive constant.

Supports the hypothesis that physical processes can be modeled by Turing machines.

Abstract

Expanding upon the widely recognized notion of mathematical universality in Turing machines, a concept of thermodynamic universality in Turing machines is introduced. Under the physical Church-Turing thesis, the existence of a thermodynamically universal Turing machine (TUTM) is demonstrated. A TUTM not only has the capability to simulate the input-output behavior of any given Turing machine but also replicate the heat production of that machine up to an additive constant. The finding shows that the hypothesis that the physical world is simulated by Turing machines may not be completely absurd.