Semi-Classical Subspaces, The No Synchronization Law, and More

TL;DR

This paper explores the interface of algorithmic information theory and physics, introducing semi-classical subspaces and the No Synchronization Law to understand quantum-classical barriers and thermodynamic entropy behavior.

Contribution

It introduces the concept of semi-classical subspaces and the No Synchronization Law, advancing understanding of quantum-classical boundaries and entropy synchronization constraints.

Findings

Partial signals and information cloning possible in semi-classical subspaces

Separate systems cannot have synchronized algorithmic thermodynamic entropies

Theoretical links between Kolmogorov complexity and black hole physics

Abstract

This paper looks at the intersection of algorithmic information theory and physics, namely quantum mechanics, thermodynamics, and black holes. We discuss theorems which characterize the barrier between the quantum world and the classical realm. The notion of a ``semi-classical subspace'' is introduced. Partial signals and partial information cloning can be obtained on quantum states in semi-classical subspaces. The No Synchronization Law is detailed, which says separate and isolated physical systems evolving over time cannot have algorithmic thermodynamic entropies that are in synch. We look at future work involving the Kolmogorov complexity of black holes.