The second principle of thermodynamics in a statistical context

Increase of entropy

Due to chaotic behaviour, two points with close initial conditions will spread. Volume in coarse grained phase space increases. The system will occupy all of its available volume in phase space.

Irreversibility

Fundamental laws of nature are revesible. But most of macroscopic phenomenon seems irreversible. How to solve this paradox? On large scales, reversibility is not impossible, it’s just extremely unlikely.