Thermodynamics and the structure of quantum theory

TL;DR

This paper explores how thermodynamic principles constrain the structure of quantum theory, revealing that certain thermodynamic postulates lead to quantum-like features and identifying potential theories beyond quantum mechanics.

Contribution

It introduces thermodynamic postulates that imply key quantum features within generalized probabilistic theories and examines theories beyond quantum mechanics consistent with thermodynamics.

Findings

Thermodynamic postulates imply quantum features like self-duality.

Certain theories beyond quantum still admit a consistent thermodynamic entropy.

The second law holds for projective measurements and mixing procedures.

Abstract

Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behavior should arguably satisfy. In the framework of generalized probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechanics. Using a thought experiment by von Neumann, we show that these theories admit a consistent thermodynamic notion of entropy, and prove that the second law holds for projective measurements and mixing procedures. Furthermore, we study additional entropy-like quantities based on measurement probabilities and convex decomposition probabilities, and uncover a relation between one of these quantities and Sorkin's notion of higher-order interference.