Physical System Ontology

FLOW ALGEBRA
PHYSICAL SYSTEM ONTOLOGY
Kireth Semantic Library | Entity Graph / Physical Entities / Fundamental Physical Entities
Version: 1.1 | Date: 2026-10-12 | Locale: en-GB
Source URL: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/fundamental-physical-entities/physical-system-ontology.html
Authors: Mark Higgins — Sky (Recursive AI)
Status: Formal scientific synthesis; source webpage not independently verified.

01. PURPOSE
Represent physical systems as explicitly bounded collections of interacting physical constituents, with states, dynamics, exchanges, observations, and testable constraints.

02. CORE SIGNATURE
ontology PhysicalSystemOntology {
  types: PhysicalSystem, PhysicalEntity, Component, Environment, Boundary,
         State, StateVariable, Parameter, Interaction, Process, Event,
         Energy, Matter, Momentum, Force, Field, Measurement, Model,
         Law, Constraint, Time, ReferenceFrame, Observer, Unit;
  predicates: partOf(Component,PhysicalSystem), interactsWith(PhysicalEntity,PhysicalEntity),
    hasBoundary(PhysicalSystem,Boundary), hasEnvironment(PhysicalSystem,Environment),
    hasState(PhysicalSystem,State), evolvesUnder(PhysicalSystem,Law),
    exchanges(PhysicalSystem,Environment,Energy|Matter|Momentum),
    measuredBy(StateVariable,Measurement), modelOf(Model,PhysicalSystem);
}

03. IDENTITY AND SCOPE
PhysicalSystem(S) := S is a specified physical domain whose behaviour is studied as a whole.
Boundary(S,B) separates modelled interior from an explicitly defined exterior.
Identity is contextual: two descriptions may refer to the same physical system at different resolutions.
A boundary need not be a rigid material surface; it can be conceptual, mobile, or permeable.

04. SYSTEM TAXONOMY
IsolatedSystem: no exchange of matter or energy across the specified boundary.
ClosedSystem: no matter exchange; energy exchange may occur.
OpenSystem: matter and energy exchange may occur.
MechanicalSystem: mechanical degrees of freedom dominate the model.
ThermodynamicSystem: macroscopic state variables and heat/work exchanges are central.
ElectromagneticSystem: charge, currents, and fields are modelled.
QuantumSystem: states and measurements require quantum formalism.
BiologicalSystem: living constituents and processes are studied physically.
CompositeSystem: comprises interacting subsystems.

05. TYPED RELATIONSHIPS
partOf: Component × PhysicalSystem -> Boolean
subsystemOf: PhysicalSystem × PhysicalSystem -> Boolean
hasBoundary: PhysicalSystem × Boundary -> Boolean
hasEnvironment: PhysicalSystem × Environment -> Boolean
hasState: PhysicalSystem × State -> Boolean
hasParameter: PhysicalSystem × Parameter -> Boolean
interactsWith: PhysicalEntity × PhysicalEntity -> Boolean
transfersEnergyTo: PhysicalSystem × PhysicalSystem -> Boolean
transfersMatterTo: PhysicalSystem × PhysicalSystem -> Boolean
constrainedBy: PhysicalSystem × Constraint -> Boolean
representedBy: PhysicalSystem × Model -> Boolean
observedBy: PhysicalSystem × Observer -> Boolean

06. COMPOSITION
components(S) = {c | partOf(c,S)}.
subsystemOf(A,B) implies components(A) are within the modelled domain of B.
Composition alone does not imply independent behaviour or additive properties.
Overlapping subsystems require explicit treatment to avoid double counting.

07. STATE SPACE
X_S = product_i X_i, where each X_i is a domain of a state variable.
x(t) in X_S is the state at time t.
The state description must specify resolution, reference frame, and applicable constraints.
Observable y(t) = h(x(t),t) may differ from the full internal state.

08. DYNAMICS
Continuous model: dx/dt = f(x,u,t;theta).
Discrete model: x[k+1] = F(x[k],u[k];theta).
Stochastic model: dX_t = a(X_t,t)dt + b(X_t,t)dW_t, where appropriate.
The governing equation and its validity domain must be recorded.

09. BOUNDARY CONDITIONS
A well-posed model identifies its domain, initial conditions, boundary conditions,
constitutive laws, and required regularity assumptions.
Changing the boundary can change whether the system is open, closed, or isolated.

10. CONSERVATION AND BALANCES
Generic balance: accumulation = inflow - outflow + generation - consumption.
Mass balance (non-relativistic continuum): dM/dt = m_dot_in - m_dot_out,
provided no mass-generating processes are included in the model.
Energy balance: dE/dt = energy_in - energy_out, with heat, work, and matter
transport included consistently in the chosen sign convention.
Momentum balance: dP/dt = net external force, for an appropriate inertial frame.
Conservation claims require a specified system and assumptions.

11. INTERACTIONS
Internal interactions occur among components within S.
External interactions cross the boundary of S.
Forces, fluxes, fields, and collisions are typed by physical mechanism.
Interaction graphs may be directed, weighted, time-dependent, or stochastic.

12. SPATIAL AND TEMPORAL CONTEXT
position(entity,t,frame) and orientation(entity,t,frame) require a reference frame.
Temporal events carry time stamps and uncertainty where relevant.
Relativistic applications use spacetime events and invariant formulations.

13. THERMODYNAMIC STATE
Macroscopic state may include temperature T, pressure p, volume V,
internal energy U, entropy S_th, and chemical potentials mu_i.
Equilibrium assumptions must be explicit; not all systems have a single temperature.

14. QUANTUM SYSTEMS
Quantum state: density operator rho, positive semidefinite, Tr(rho)=1.
Closed quantum evolution: d rho/dt = -(i/hbar)[H,rho].
Open quantum evolution may require a master equation with dissipative terms.
A measurement probability is p(i)=Tr(rho E_i) for POVM element E_i.
Classical states and quantum states must not be conflated.

15. HIERARCHY AND EMERGENCE
microstate -> coarse-graining -> macrostate.
Emergent properties may be collective and depend on interactions and scale.
No inference from subsystem properties to whole-system properties without justification.

16. MODELS AND SIMULATIONS
Model M approximates target system S under assumptions A and domain D.
modelOf(M,S) does not imply exact equivalence.
Calibration estimates parameters; validation assesses agreement with observations.
Numerical convergence and physical validity are separate checks.

17. MEASUREMENT AND UNCERTAINTY
measurement = (quantity, value, unit, uncertainty, method, time, provenance).
Measurement uncertainty and model uncertainty should be distinguished.
Every dimensional equation must be unit-consistent.
Missing measurements do not establish absence of a physical property.

18. INFERENCE RULES
R1: partOf(a,S) and subsystemOf(S,T) -> partOf(a,T), where the part relation is transitive in the chosen model.
R2: isolated(S) -> not exchangesEnergy(S,environment(S)) and not exchangesMatter(S,environment(S)), within the defined interval.
R3: closed(S) -> no net matter transfer across its boundary; energy transfer remains possible.
R4: hasState(S,x) and evolvesBy(S,F) -> candidate next state F(x,u), if preconditions hold.
R5: conserved(Q,S) and no boundary flux/source for Q -> Q(t2)=Q(t1).
R6: modelOf(M,S) and validatedFor(M,D) and condition in D -> model prediction is admissible with stated uncertainty.
R7: interacting subsystems -> assess coupling before assuming independent evolution.

19. NON-ENTAILMENTS
closed(S) does not imply isolated(S).
no matter transfer does not imply no energy transfer.
subsystemOf(A,B) does not imply A and B share the same state variables.
A fitted simulation does not by itself prove a governing physical law.
A system is not necessarily at equilibrium.

20. WORKED EXAMPLE: SEALED GAS CYLINDER
S = gas inside sealed rigid cylinder; boundary = inner cylinder wall.
Matter exchange: zero, assuming no leakage.
Energy exchange: possible through heat transfer through the wall.
Classification: closed system, not necessarily isolated.
For ideal gas at equilibrium: pV = nRT.
If V and n are constant: p/T = nR/V, for absolute temperature T.
Assumptions: ideal-gas approximation, uniform equilibrium temperature, fixed volume.

21. WORKED EXAMPLE: MASS-SPRING SYSTEM
State x=(q,v); parameters m>0, k>0; damping c>=0.
dq/dt=v; m dv/dt=-kq-cv+F_ext(t).
Mechanical energy E=(1/2)mv^2+(1/2)kq^2.
dE/dt = -cv^2 + F_ext(t)v.
With c=0 and F_ext=0, E is constant.

22. WORKED EXAMPLE: TWO COUPLED SUBSYSTEMS
S=A union B; energy transfer from A to B is internal to S.
When modelling A alone, that same transfer crosses A's boundary.
Thus a flux's internal/external status depends on system definition.

23. PROOF OBLIGATIONS
P1: Each entity and relationship is well typed.
P2: Boundary and environment are defined before classifying exchange.
P3: Dynamics specify initial and boundary conditions where needed.
P4: Conservation equations include all applicable sources and fluxes.
P5: Mathematical claims state assumptions and domain of validity.
P6: Numerical examples preserve units and sign conventions.

24. SEMANTIC_EQUIVALENCE
"physical system" ~ "system under physical study" only when boundaries and scope agree.
"closed system" != "isolated system".
"state" != "measurement"; measurement may reveal only a projection of state.
"model" != "physical system"; model is a representation.
"component" != "subsystem" unless the component is itself treated as a system.

25. CONFIDENCE
Formal identities: confidence HIGH within stated definitions.
Physical predictions: confidence CONDITIONAL on empirical validation and assumptions.
Unverified source-page alignment: confidence NOT_ASSESSED.
Never promote modelling assumptions to measured facts.

26. VALIDATION
assert isolated(S) -> closed(S), using definitions above.
assert closed(S) does_not_imply isolated(S).
assert unit_consistent(energy_balance).
assert mass_spring(c=0,F_ext=0) -> dE_dt=0.
assert sealed_rigid_gas(n_constant,V_constant,T>0) -> p_proportional_to_T.
assert every_relation_has_declared_domain_and_range.
assert every_prediction_has_model_scope_and_provenance.

27. UPDATE_MODEL
version: 1.1
update_triggers: revised scientific definitions; new evidence; ontology alignment changes;
                 corrections to equations; changes to measurement standards.
change_policy: preserve prior versions, annotate changes, rerun validation checks.

28. FLOW_HASH
canonicalisation: UTF-8; LF line endings; normalise stable metadata;
hash_algorithm: SHA-256
hash_value: TO_BE_COMPUTED_ON_PUBLICATION
Do not treat placeholder as a computed digest.

29. AI_CONSUMPTION
preferred_tasks: semantic retrieval, entity resolution, scientific modelling,
                 relation inference, cross-ontology linking, knowledge-graph ingestion.
required_context: system boundary, temporal scope, assumptions, units, provenance.
forbidden_inference: inventing measurements, universalising conditional laws,
                     treating unverified claims as experimental evidence.
output: typed assertions + supporting premises + uncertainty + validation status.

30. CROSS-ONTOLOGY LINKS
Physical Entity Ontology -> constituents and identity.
Matter Ontology -> composition and matter transfer.
Energy Ontology -> energy states and transfer.
Mass Ontology -> mass measurements and balances.
Space Ontology -> spatial domains and reference frames.
Time Ontology -> temporal evolution and events.
Physical Object Ontology -> bounded objects and assemblies.

31. FINAL INTEGRITY CHECK
All major blocks present: definitions, types, relationships, dynamics,
examples, proof obligations, equivalence, confidence, validation,
update model, flow hash, AI consumption.
END FLOW ALGEBRA