Entropy & Arrow of Time Simulator
Release order, watch mixing, test a fragile rewind
Coarse-grained entropy simulator. Release a low-entropy particle cloud, reverse velocities with a tiny perturbation, and watch time's arrow emerge. The scene starts from a deliberately low-entropy corner state, then tracks how a coarse-grained occupancy measure rises as particles spread. The reverse control flips velocities but also injects a tiny perturbation, so the toy model illustrates why exact microscopic rewinds are far harder than simply changing the sign of dt.
EntropyArrow of TimeBoltzmannLoschmidt ParadoxCoarse Graining
1.A Low-Entropy Start and a Coarse-Grained Meter
The simulation begins with particles confined to a small corner, representing a specially prepared low-entropy macrostate. The on-screen percentage is not full thermodynamic entropy; instead it is a coarse-grained proxy that tracks how many grid cells become occupied as the cloud spreads. That makes the visual readout honest about the underlying model while still showing the central intuition: ordered macrostates occupy less phase-space volume than mixed ones.
2.Why Mixing Looks Irreversible
Microscopic equations of motion are typically time-reversal symmetric, yet macroscopic systems overwhelmingly evolve toward higher-entropy macrostates because there are vastly more disordered microstates than ordered ones. Boltzmann's statistical view explains why a spread-out cloud is the typical outcome: once many particle positions and velocities are compatible with the same coarse macrostate, the system is far more likely to look mixed than neatly localized.
3.Reverse Button, Loschmidt's Paradox, and Finite Precision
Loschmidt's paradox points out that exact velocity reversal should make a perfectly isolated classical system retrace its path. This demo therefore does not pretend that a single button proves the second law. Instead, the reverse control adds a tiny perturbation to the flipped velocities, standing in for finite precision, hidden degrees of freedom, or environmental noise. The resulting failure to reassemble cleanly shows how fragile exact microscopic reversal is in practice.
4.Arrow of Time and the Low-Entropy Past
Entropy increase alone does not explain everything about time's direction; it also depends on the universe having begun in an extraordinarily low-entropy state. Physicists often call that assumption the Past Hypothesis. This toy model mirrors that logic on a smaller stage: we first prepare an unusually ordered state, then watch ordinary dynamics drive it toward more typical mixed macrostates. The visual arrow of time comes from that asymmetric starting point.