Ten Proofs of the Generalized Second Law

TL;DR

This paper reviews and critiques ten different proofs of the Generalized Second Law of Thermodynamics, offering new insights and strategies for future, more comprehensive proofs, while discussing foundational choices and regimes in the theory.

Contribution

It provides a critical analysis of existing proofs of the GSL and introduces new perspectives and strategies for developing more complete proofs.

Findings

Identifies limitations in current proofs of the GSL

Proposes new strategies for future proofs

Clarifies definitions of regimes and foundational choices

Abstract

Ten attempts to prove the Generalized Second Law of Thermodyanmics (GSL) are described and critiqued. Each proof provides valuable insights which should be useful for constructing future, more complete proofs. Rather than merely summarizing previous research, this review offers new perspectives, and strategies for overcoming limitations of the existing proofs. A long introductory section addresses some choices that must be made in any formulation the GSL: Should one use the Gibbs or the Boltzmann entropy? Should one use the global or the apparent horizon? Is it necessary to assume any entropy bounds? If the area has quantum fluctuations, should the GSL apply to the average area? The definition and implications of the classical, hydrodynamic, semiclassical and full quantum gravity regimes are also discussed. A lack of agreement regarding how to define the "quasi-stationary" regime is addressed by distinguishing it from the "quasi-steady" regime.