Entropy Arrow of Time & Thermodynamic Clock Simulator

Boltzmann Entropy S 0.00 J/K S = kB · ln(Ω)

Entropy Production ΔS +0.00 J/K Irreversible dissipation

Extracted Work W 0.00 J Piston mechanical yield

Entropic Time τ 0.00 s τ(ΔS) = (ΔS/λ)^(1/γ)

Physical Insight: As stated in the International Journal of Theoretical Physics (2025) research, in timeless relational physics, coordinate time t is an abstraction. The physical arrow of time τ is driven monotonically by microstate phase-space spreading: $\tau(\Delta S) = (\Delta S / \lambda)^{1/\gamma}$. Once partition mixing ceases and the system reaches maximum thermal equilibrium, $\Delta S \to 0$: no further heat engine work can be extracted, and macroscopic physical change comes to an absolute halt.

Emergent Entropic Clock Internal Relational τ

τ(ΔS) = (ΔS / 0.12)^(1/1.5)

Clock hand advances only while entropy is produced. At equilibrium, the clock freezes.

Phase-Space Controls

Left Temp: 370 K

Right Temp: 295 K

Particles (L): 120

Particles (R): 40

Partition Aperture: 0%

Speed Distribution (v) Maxwell-Boltzmann

Heat Piston: Idle (Awaiting Gradient)