A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices

TL;DR

This paper proves the generalized second law for quantum fields across causal horizons, allowing for rapid time variations and arbitrary horizon slices, under specific algebraic axioms verified for free and conformal fields.

Contribution

It extends the proof of the generalized second law to more general, rapidly changing quantum fields and arbitrary horizon slices, using a set of verified algebraic axioms.

Findings

Entropy increases between any two horizon slices.

Axioms verified for free fields and conformal theories.

Discussion on applicability to interacting theories.

Abstract

The generalized second law is proven for semiclassical quantum fields falling across a causal horizon, minimally coupled to general relativity. The proof is much more general than previous proofs in that it permits the quantum fields to be rapidly changing with time, and shows that entropy increases when comparing any slice of the horizon to any earlier slice. The proof requires the existence of an algebra of observables restricted to the horizon, satisfying certain axioms (Determinism, Ultralocality, Local Lorentz Invariance, and Stability). These axioms are explicitly verified in the case of free fields of various spins, as well as 1+1 conformal field theories. The validity of the axioms for other interacting theories is discussed.