Probabilistic Turing Machine and Landauer Limit

TL;DR

This paper establishes a theoretical equivalence between probabilistic Turing machines and one-dimensional Ising models, enabling entropy evaluation at computation's end and confirming the Landauer limit.

Contribution

It introduces a novel mapping between a physical spin system and computational processes, linking thermodynamics and computation.

Findings

Equivalence between probabilistic Turing machines and 1D Ising models.

Entropy at computation's end aligns with Landauer limit.

Provides a physical interpretation of computational entropy.

Abstract

We show the equivalence between a probabilistic Turing machine and the time evolution of a one-dimensional Ising model, the Glauber model in one dimension, equilibrium positions representing the results of computations of the Turing machine. This equivalence permits to map a physical system on a computational system providing in this way an evaluation of the entropy at the end of computation. The result agrees with Landauer limit.