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State Space

Definition

A state space is the set of all physically admissible states a system can occupy, together with the variables required to specify those states and the rules governing transitions between them.

Each point in state space represents a complete specification of the system at a given moment.

Ontic / Core Claim

State space is not a mathematical convenience alone; it reflects the real degrees of freedom and constraints of a physical system.

System dynamics correspond to trajectories through state space.
Constraints restrict accessible regions.
Distinctions correspond to partitions of state space that condition future trajectories.

Changes to system structure, coupling, or environment modify the effective state space by adding, removing, or constraining dimensions.

Distillation

State space is the arena in which distinctions, persistence, and records exist.

Why it matters

• Dynamics: Makes change, stability, and evolution precise.
• Distinction: Provides the substrate partitions are made in.
• Persistence: Allows metastability to be defined geometrically and dynamically.
• RDD coherence: Prevents informal talk of “states” without specifying degrees of freedom.

Links

• Related atoms:

  • Distinction
  • Persistent Distinction
  • Record (Memory Substrate)
  • Symmetry Breaking
  • Constraint

• Used in molecules:

  • (none yet)

• Conflicts with:

  • Informal or purely epistemic notions of “state”

Sources

• Source: Goldstein, H. (2000). Classical mechanics (2. ed., 32. [Nachdr.]). Addison-Wesley.

  • Key: @goldsteinClassicalMechanics2000
  • Use here: Canonical definition of state space in classical dynamical systems.

• Source: Strogatz, S. (2019). Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering (Second edition, first issued in hardback). CRC Press.

  • Key: @strogatzNonlinearDynamicsChaos2019
  • Use here: Trajectories, attractors, and stability in state space.

• Source: Sethna, J. P. (2021). Statistical Mechanics: Entropy, Order Parameters, and Complexity.

  • Key: @sethnaEntropyOrderParameters2021
  • Use here: State space under thermodynamic and statistical constraints.

Re-contextualization Log

• 2025-12-26 · context: Required foundation for Distinction and Persistence
  effect: created
  note: Formalized state space as an ontic substrate for partitions, dynamics, and constraints.