Energy Flux Tracking & Information Theory Foundation

[M1thieu]

Objective

• Add energy flux tracking to enable sustained energy flows vs instantaneous transfers
• Implement information theory foundation (Shannon entropy, mutual information, KL divergence)
• Fix code duplication and naming inconsistencies
• Supports Electromagnetic System Minimal Implementation #111 by providing energy foundation infrastructure
• Advances Material Point Method (MPM) Integration for Unified Physics System #76 by adding energy conservation tracking

Implementation

Energy Flux Tracking:

• Extended EnergyTransaction with transfer_rate and duration fields
• Added flux analytics to EnergyAccountingLedger for flow pattern analysis
• Added create_flux_transaction() method for sustained energy transfers

Information Theory:

• Shannon entropy with conditional and joint calculations
• KL divergence, Jensen-Shannon divergence for distribution comparison
• Mutual information with bias correction for emergent behavior analysis

Code Quality:

• Consolidated duplicate EnergyType definitions
• Renamed create_standing_wave → create_standing_wave_parameters for accuracy
• Removed unused spacetime crate (delegated to Bevy)

Testing

• All crates compile without breaking changes
• Energy flux integrates seamlessly with existing conservation system
• Information theory handles edge cases properly

Visual Changes

// Track energy flows over time
let flux = energy_system.create_flux_transaction(50.0, 10.0, source, target, time);
let avg_rate = ledger.average_transfer_rate(60.0);

// Measure system complexity
let entropy = Shannon::entropy(&behavior_data);
let mutual_info = MutualInfo::discrete(&states_a, &states_b);

Technical Notes

Compatibility: Fully backward compatible

Future Ready: Foundation prepared for physics engine integration

Limitations: Flux assumes linear transfer rates, information theory needs adequate sample sizes