Information transport in classical statistical systems

TL;DR

This paper explores how classical statistical systems called static memory materials can propagate information through boundary-dependent bulk properties, acting as quantum simulators with wave function-like descriptions and unitary evolution.

Contribution

It introduces a framework using classical wave functions to describe information transport in static memory materials, linking classical statistical mechanics with quantum-like evolution equations.

Findings

Classical wave functions obey superposition and bilinear probability structures.

Evolution within subsectors is unitary, resembling quantum time evolution.

Certain Ising models can simulate relativistic fermion dynamics.

Abstract

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schr\"odinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.