Entropy augmentation through subadditive excess: information theory in irreversible processes

TL;DR

This work addresses the challenge of reconciling microscopic reversible dynamics with macroscopic irreversibility by reframing the Stoßzahlansatz through information theory. It introduces the EASE principle, which uses a decorrelating projector $\mathcal{P}$ to produce entropy augmentation via subadditive excess and derives a nonlinear Nakajima–Zwanzig equation for the relevant density $W_{\mathcal{P}}$ alongside a residual $W_{\mathcal{Q}}$. A memory-limited extension, EASE-L, provides a linear, tractable set of equations that capture correlations within a finite memory window $\tau^*$, enabling efficient numerical implementations. The framework generalizes the Boltzmann H-theorem to broad dynamical decompositions, offering a principled route to simulate irreversible dynamics in classical and quantum settings using tensor-network or related methods, while clarifying the distinction between information entropy and thermodynamic entropy in nonequilibrium regimes.

Abstract

Within its range of applicability, the Boltzmann equation seems unique in its capacity to accurately describe the transition from almost any initial state to a self-equilibrated thermal state. Using information-theoretic methods to rephrase the key idea of Maxwell and Boltzmann, the Stoßzahlansatz, a far more general, abstract ansatz is developed. An increase of the Gibbs-Shannon-von Neumann entropy results without the usual coarse-graining. The mathematical structure of the ansatz also provides avenues for efficient computation and simulation.