On the Conservation of Structure

Key Points

• The research aims to define and formalize the concept of structure as a conserved quantity in dynamic systems.
• Proposes a constrained quantity called structure under admissible dynamics.
• Formalizes structure as a path-dependent functional over state space.
• Derives conditions for conservation and dissipation bounds related to structural density.
• Introduces a generalized continuity equation for structural density.
• Demonstrates that time evolution can be seen as minimizing structural cost within an energy budget.
• Establishes that selection represents the measurable rate of structural filtering.