On the generic increase of entropy in isolated systems

TL;DR

This paper presents a universal framework for understanding entropy production in isolated quantum systems, showing that entropy generically increases due to many-body interactions through energy broadening and temporal coarse-graining.

Contribution

It introduces a resolvent-based hierarchical ansatz approach to model entropy distribution, revealing universal pathways and scaling laws for entropy generation in quantum many-body systems.

Findings

Entropy scales logarithmically with interaction strength.

Numerical simulations confirm the universal entropy growth laws.

Unified description of entropy distribution via hybrid ansatz.

Abstract

This study establishes a universal mechanism for entropy production in isolated quantum systems governed by interactions that induce random-phase fluctuations. By developing a resolvent-based framework, we demonstrate that steady-state entropy generically arises from many-body interactions, independent of specific coupling details, provided the coherent accumulation of systematic biases does not overwhelm the random-phase fluctuations. Analytical arguments reveal that entropy generation is driven by two universal pathways: interaction-induced energy broadening and temporal coarse-graining over exponentially small energy gaps. To quantitatively capture the probability distribution, we introduce a hierarchical ansatz approach. A Lorentzian ansatz models the bulk region, leading to self-consistent equations for the broadening and shift parameters, and yields a logarithmic entropy scaling with interaction strength. For the tail behavior, a Gaussian ansatz is formulated, and the corresponding self-consistent condition is derived and validated. By further combining these profiles into an enhanced Lorentzian-Gaussian hybrid ansatz, we achieve a unified and refined description of the full distribution. Numerical simulations of nonintegrable Ising spin chains confirm the predicted logarithmic entropy scaling and validate the self-consistent equations. Our framework effectively bridges the concepts of observational entropy and von Neumann entropy dynamics, providing predictive tools for thermodynamic behavior in quantum many-body systems. These results resolve longstanding debates about interaction-dependent entropy scaling and offer pathways for entropy control in quantum technologies.