From Order to Entropy: How Gravity Shapes Time's Arrow

This educational handout by Matthew J. Hall, created with assistance from GPT-5 Thinking, provides a clear, step-by-step introduction to the relationship between entropy, gravity, and the arrow of time.
Written in plain language for students and general readers, it explains how microscopic dynamics and coarse-graining produce the Second Law of Thermodynamics, how gravity bends entropy toward clumping, and how black holes force us to include geometry in thermodynamic reasoning.
Each section pairs mathematical expressions with plain-English explanations, showing how the arrow of time emerges from low-entropy initial conditions and evolves through statistical and geometric processes.
This work forms part of Hall’s broader educational series on time, gravity, and dynamics, connecting thermodynamics, cosmology, and relativity.

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