Coherence Dynamics and Temporal Structure

This project presents a testable theoretical framework in which temporal structure emerges from the dynamics of coherence, defined as the difference between a system’s maximum possible entropy and its actual entropy. The work introduces temporal density as a measure of how rapidly a system moves through its coherence landscape. The manuscript develops a general evolution equation that separates constraint‑driven changes from entropy‑producing processes. This formulation applies across classical, quantum, and non‑equilibrium systems. A worked ideal‑gas example shows that fast expansions generate coherence gradients an order of magnitude larger than slow expansions under identical conditions, providing a clear experimental signature. The paper compares this framework with thermodynamics, decoherence theory, and the thermal time hypothesis, and proposes experimental tests in both quantum and classical settings. Appendices supply detailed derivations and supporting mathematical structures. The work concludes with a set of open problems that outline a path toward extending the framework into statistical field theory, quantum field theory, and gravitational contexts.