On the generic increase of entropy in isolated systems

This study establishes a universal mechanism for entropy production in isolated quantum systems governed by the eigenstate thermalization hypothesis (ETH). By developing a resolvent-based framework, we demonstrate that steady-state entropy generically arises from many-body interactions, independent of specific coupling details. 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. Numerical simulations of nonintegrable Ising spin chains confirm logarithmic entropy scaling, consistent with predictions derived from ETH-governed eigenstate mixing. The derived self-consistent equations for energy shift and broadening parameters agree closely with numerical results. These results unify observational entropy concepts with von Neumann entropy dynamics, providing predictive tools for thermodynamic behavior in quantum many-body systems. Our findings resolve longstanding debates about interaction-dependent entropy scaling and offer pathways for entropy control in quantum technologies.