A precise formulation of the third law of thermodynamics

TL;DR

This paper provides a rigorous formulation of the third law of thermodynamics, establishing the inaccessibility of zero-temperature states and their adiabatic equivalence, with implications for quantum systems and black holes.

Contribution

It offers a precise, mathematically rigorous statement of the third law, extending its validity to quantum and quantum field systems, and discusses open problems for black holes.

Findings

Zero-temperature states are physically adiabatically inaccessible from finite-temperature states.

All zero-temperature states are adiabatically equivalent under certain conditions.

The third law is universally valid for quantum-mechanical macroscopic systems.

Abstract

The third law of thermodynamics is formulated precisely: all points of the state space of zero temperature $\Gamma_0$ are physically adiabatically inaccessible from the state space of a simple system. In addition to implying the unattainability of absolute zero in finite time (or "by a finite number of operations"), it admits as corollary, under a continuity assumption, that all points of $\Gamma_0$ are adiabatically equivalent. We argue that the third law is universally valid for all macroscopic systems which obey the laws of quantum mechanics and/or quantum field theory. We also briefly discuss why a precise formulation of the third law for black holes remains an open problem.