Arrow of Time & Thermodynamic Entropy Lab S = k ln W

Time Elapsed: 0.00s
Entropy S / k
0.00
Microstates W
1
Temp Left (K)
300
Temp Right (K)
100
Presets
System Configuration
Particles (Left / Right) 100 / 100
Initial Temp Ratio (T1/T2) 3.0x
Grid Resolution (Microstate Binning) 8 x 8
Visualization Overlay
Show Microstate Grid
Show Velocity Vectors
Thermographic Color
Boltzmann Entropy Principle:
Microscopic particle interactions are deterministic and time-reversible. However, macroscopic systems spontaneously evolve towards the macrostate with the highest number of microstates ($W$), giving rise to the irreversible Arrow of Time ($S = k \ln W$).

Entropy, Coarse Graining and Velocity Reversal

Read the explanation

This entropy lab counts particles in spatial grid bins. Its actual formula is N log N minus the sum of each occupied count times log of that count. This is a Stirling approximation to log of a multinomial count, rather than an exact factorial calculation. Consider four particles. Counts four and zero give zero. Counts two and two give four log two, about two point seven seven three. The bars use one hundred eighty pixels per unit of S divided by k. Spreading counts raises this coarse spatial measure without creating particles. Grid resolution changes the question being counted. If the same four particles occupy one bin, the proxy is zero. If a finer grid resolves four different occupied bins with one particle each, it is four log four, about five point five four five. These two cases keep the total particle number fixed. This is a coarse graining effect, not a claim that changing a display switch injects heat. In the source, grid resolution changes spatial binning. Show Grid changes only the overlay, and leaves the entropy formula unchanged. Reverse Velocity negates both components of every particle velocity. For an illustrative vector three and four, the reversal is minus three and minus four. Both have squared speed twenty five. The source temperature proxy averages squared speed and multiplies by fifty, so instantaneous reversal leaves that proxy unchanged. Removing the partition changes wall constraints. Pause stops physics updates while controls remain available. The export is the complete recorded history with time, entropy and left and right temperature columns. Finite collision steps and overlap correction mean this numerical simulation is not a proof of exact trajectory retracing.

Super generates helpful tools and automates fact-checking across the internet proactively. If you enjoyed this tool, build your own with Super and share it with a friend.