Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces

TL;DR

This paper proves large deviation principles and fluctuation theorems for invariant measures on shift spaces under general decoupling conditions, extending thermodynamic formalism to new contexts like quantum measurements.

Contribution

It establishes LDPs and fluctuation relations for measures with decoupling conditions beyond thermodynamic formalism, applicable in multifractal and quantum measurement settings.

Findings

Proved Level-1 and Level-3 LDPs for invariant measures

Derived Fluctuation Relation for entropy production

Extended large deviation theory to non-thermodynamic decoupling conditions

Abstract

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such decoupling conditions arise naturally in multifractal analysis, in Gibbs states with hard-core interactions, and in the statistics of repeated quantum measurement processes. We also prove the LDP for the entropy production of pairs of such measures and derive the related Fluctuation Relation. The proofs are based on Ruelle-Lanford functions, and the exposition is essentially self-contained.