Entropy Coordinates in Physical Simulation
This model introduces the concept of "entropy coordinates" to the field of physical simulation, ensuring that each physical simulation transformation corresponds to a computable entropy coordinate. Traditional simulation methods often treat entropy as a consequence rather than a driving factor of system evolution, whereas the proposed entropy coordinate framework provides thermodynamic coordinates for physical simulation—embedding entropy itself as a fundamental coordinate into the core architecture of physical simulation. This approach, based on discrete spacetime quantum units (SEQ), not only redefines the mathematical representation of time and space but also offers new theoretical foundations and implementation pathways for simulating complex systems. It enables the observation of differences in physical processes along varying entropy-increasing paths during simulations.
Core Principles of Entropy Coordinates: From Thermodynamic Laws to Simulation Architecture.
The mathematical essence of the entropy coordinate framework lies in transforming the classical second law of thermodynamics into an active simulation-driving mechanism. In this model, the system's entropy is no longer expressed through the traditional logarithmic form but instead adopts a multiplicative form: S = ∏mᵢ
where mᵢ represents the energy magnitude carried by the i-th Space Elementary Quantum (SEQ). This definition offers three key advantages:
1. Automatic satisfaction of entropy increase law: Closed systems naturally evolve toward maximizing the product
2. Built-in temporal directionality: The growth direction of entropy coordinates explicitly corresponds to the arrow of time
3. Numerical stability: The multiplicative form under energy conservation constraints has finite upper bounds, avoiding divergence issues in conventional entropy calculations
As fundamental coordinates for physical simulation, entropy not only describes system states but directly determines evolutionary paths. When computer models of the universe adopt this framework, the first and second laws of thermodynamics combined with the principle of least action become the primary drivers of system evolution, transforming entropy from a passive metric into an active coordinate. These entropy coordinates provide a thermodynamic observation perspective for comparing different evolutionary paths in physical simulations.
