physics

Thermodynamics & Statistical Mechanics

The physics of heat, energy, and entropy — from the arrow of time to the fundamental limits of engines and information.

thermodynamicsentropyBoltzmannMaxwellCarnotstatistical mechanics

Thermodynamics is the branch of physics that deals with heat, work, temperature, and entropy. It governs everything from the efficiency of engines to the fate of the universe. The four laws of thermodynamics are among the most fundamental and universally applicable principles in all of physics.

Statistical mechanics, developed by Boltzmann, Maxwell, and Gibbs in the late 19th century, explains thermodynamics from the bottom up — showing how the macroscopic properties of matter (temperature, pressure, entropy) emerge from the microscopic behavior of atoms and molecules. Boltzmann's insight that entropy equals k_B × ln(W) connects the deterministic world of particles to the probabilistic arrow of time.

These simulations let you explore the key ideas of thermodynamics and statistical mechanics: watch entropy increase in real time, see how molecular speeds distribute according to Maxwell-Boltzmann, understand why no engine can beat Carnot efficiency, and confront the mind-bending Boltzmann brain paradox.

4 interactive simulations

calculator

Boltzmann Brain Timescale Calculator

Explore the mind-bending timescales of thermal fluctuations — how long until random chance assembles a conscious brain from the void

calculator

Carnot Cycle Efficiency Calculator

Visualize the Carnot cycle on a PV diagram and calculate the theoretical maximum efficiency of any heat engine operating between two temperatures

calculator

Entropy & Particle Diffusion Simulator

Watch particles diffuse from order to disorder and observe entropy increase in real time — a visual demonstration of the Second Law of Thermodynamics

calculator

Maxwell–Boltzmann Speed Distribution

Explore how temperature and molecular mass shape the distribution of particle speeds in a gas — and why some molecules escape Earth's gravity