Poincaré Recurrence Simulation

The Poincaré recurrence theorem states that certain systems will, after a sufficiently long but finite time, return to a state very close to their initial state. This project provides visual simulations to help demystify and intuitively explain this profound mathematical and physical concept.

Classical Recurrence

The classical simulation demonstrates the theorem using an idealized, closed thermodynamic system—such as gas particles in a sealed box. By tracking the phase space trajectory of these particles, the simulation visually proves how, given enough time, the particles will inevitably arrange themselves in a configuration nearly identical to their starting positions.

Quantum Recurrence

The quantum simulation explores the quantum analogue of the theorem. It visualizes the time evolution of a closed quantum system governed by a discrete energy spectrum. By plotting the evolution of the wave function and the expectation values of observables, the simulation highlights the quasi-periodic nature of quantum states, demonstrating how the system returns to its initial state over the Poincaré recurrence time.

This project bridges the gap between abstract mathematical theorems and intuitive physical understanding through interactive, browser-based visualizations.