Reset Dynamics, Paper 15: Emergent Time and Irreversibility from Structural Phase Transitions

This paper is the capstone of the Reset Dynamics series , presenting a unified framework in which time and irreversibility emerge from structural phase transitions. Within the Reset Dynamics framework, we introduce a minimal dynamical system with three state variables: dissipation entropy S(t), structural complexity M(t), and control activity A(t). The threshold-induced Reset operator corresponds to a phase transition at the consistency ratio R = Γ/C = 1. Temporal directionality is interpreted as a counting process of irreversible Reset events, formalized as a Poincaré crossing index on the state space. Key contributions include:- Three temporal scales: phase time (scaffolding), repetition time, and discrete macroscopic Reset time- A Lyapunov–information functional L = S + α·dim(H¹) characterizing irreversibility- Explicit comparison with Page–Wootters, Barbour, Rovelli, and Landauer frameworks- Parameter constraints and a numerical illustration of Reset cycles- Falsifiable predictions, including discrete macroscopic time and stepwise entropy increase This is a working capstone edition (Version 2.0), revised in response to peer feedback from open review. The paper does not claim to have "proven the origin of time" for all physical systems, but offers a self-consistent, testable effective theory within the Reset Dynamics framework. All papers in the Reset Dynamics series are archived on Zenodo under the UOSSF project.