Energy Ontology

FLOW ALGEBRA
ENERGY ONTOLOGY — FUNDAMENTAL PHYSICAL ENTITIES
Version: 1.1
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/fundamental-physical-entities/energy-ontology-2.html
Authors: Mark Higgins — Sky (Recursive AI)
Project: Kireth Semantic Library | https://kirethresearch.org
Status: Formal scientific synthesis; source webpage not independently verified.

01. PURPOSE
Represent energy as a measurable physical quantity associated with systems, states, fields and interactions. Specify energy accounting, transfer, transformation and conservation under explicit assumptions.

02. SCOPE
Classical mechanics, thermodynamics, electromagnetism, relativity and quantum physics; exclude unsupported claims that energy is a material substance.

03. TYPE SYSTEM
TYPE PhysicalSystem
TYPE PhysicalState
TYPE Process
TYPE Interaction
TYPE EnergyQuantity : RealWithUnit[J]
TYPE PowerQuantity : RealWithUnit[W]
TYPE TimeInterval : RealWithUnit[s]
TYPE WorkQuantity : RealWithUnit[J]
TYPE HeatTransfer : RealWithUnit[J]
TYPE ReferenceFrame
TYPE Boundary
TYPE ModelAssumption
TYPE Measurement
TYPE Uncertainty
TYPE Evidence

04. CORE ENTITY
ENTITY Energy
  dimension: M L^2 T^-2
  SI_unit: joule (J)
  kind: scalar physical quantity
  assigned_to: physical system or state relative to model and reference convention
  accounting: energy changes by transfers and interactions

05. RELATIONSHIP SIGNATURES
HAS_ENERGY(PhysicalSystem, PhysicalState, EnergyQuantity)
UNDERGOES(PhysicalSystem, Process)
TRANSFERS_ENERGY(PhysicalSystem, PhysicalSystem, EnergyQuantity, Process)
PERFORMS_WORK(PhysicalSystem, PhysicalSystem, WorkQuantity)
EXCHANGES_HEAT(PhysicalSystem, PhysicalSystem, HeatTransfer)
HAS_BOUNDARY(PhysicalSystem, Boundary)
MEASURED_BY(EnergyQuantity, Measurement)
VALID_UNDER(Proposition, ModelAssumption)
SUPPORTED_BY(Proposition, Evidence)

06. DIMENSIONAL RULES
[J] = kg m^2 s^-2
[W] = J s^-1
Energy values may be added only when expressed in compatible units and conventions.
Energy and power are distinct types.

07. ENERGY FORMS
Kinetic energy: E_k = (1/2) m v^2 (nonrelativistic).
Gravitational potential near Earth: U_g = m g h (constant g approximation).
Elastic potential: U_s = (1/2) k x^2 (Hooke-law spring).
Thermal internal energy: U; state-dependent, not identical to heat transfer.
Electromagnetic field energy: integral of energy density over volume.
Rest energy: E_0 = m c^2.
Photon energy: E = h nu.
Chemical and nuclear energy: changes in system energy from state transformations.

08. STATE AND REFERENCE CONVENTIONS
Potential energy may depend on chosen zero level.
Kinetic energy depends on reference frame.
Only compare numerical energies under compatible frame, system boundary and reference conventions.

09. CLASSICAL WORK
For force F acting along displacement path C:
W = integral_C F · dr.
If force is constant and parallel to displacement: W = F d.
Work-energy theorem for a particle: Delta K = W_net.

10. POWER
Average power: P_avg = Delta E / Delta t.
Instantaneous power: P = dE/dt for a specified transfer or conversion rate.
Mechanical power: P = F · v when applicable.

11. THERMODYNAMIC ACCOUNTING
Convention: Q positive into system; W positive when done by system.
First law for closed system: Delta U = Q - W, with kinetic/potential changes handled separately or within total energy accounting.
For an isolated system with no external energy exchange: Delta E_total = 0.
Heat is energy transfer driven by temperature difference, not a stored substance.

12. CONSERVATION
For an isolated system whose governing physics is time-translation invariant, total energy is conserved.
For a control volume, accumulation = energy inflow - energy outflow + applicable sources.
In general relativity, global conserved energy is not guaranteed for arbitrary curved spacetimes; local stress-energy conservation is expressed covariantly.

13. MECHANICAL ENERGY
E_mech = K + U.
If only conservative forces do work, Delta E_mech = 0.
With nonconservative forces: Delta E_mech = W_nonconservative.

14. FIELD ENERGY
Electromagnetic vacuum energy density: u = (epsilon_0/2)|E|^2 + (1/(2 mu_0))|B|^2.
Poynting vector: S = (1/mu_0) E × B.
Poynting theorem relates local field energy changes, flux and work on charges.

15. RELATIVISTIC ENERGY
E^2 = (pc)^2 + (m c^2)^2 for a free particle.
At rest: p = 0 => E = m c^2.
Massless particle: E = pc.
Do not substitute classical kinetic energy outside its approximation regime.

16. QUANTUM ENERGY
Observable energy is represented by Hamiltonian operator H.
Stationary states satisfy H|psi_n> = E_n|psi_n>.
Measurement outcomes are eigenvalues subject to the model and operator domain.
For a photon: E = h nu.

17. ENERGY TRANSFER
TRANSFER(system_a, system_b, q): outgoing energy from a and incoming energy to b are equal in magnitude for an ideal accounting boundary, absent additional reservoirs or losses.
Energy can change form; 'loss' in engineering normally denotes transfer to less useful forms or surroundings, not destruction of energy.

18. EFFICIENCY
eta = useful_energy_output / total_energy_input for a defined device and accounting period.
0 <= eta <= 1 for ordinary energy-conversion efficiency under consistent accounting.
Distinguish energy efficiency from coefficient of performance of heat pumps, which may exceed 1.

19. ENTROPY DISTINCTION
Energy conservation does not imply reversibility.
Second-law constraints determine the direction and usefulness of energy transformations.
Entropy and energy are distinct physical quantities.

20. INFERENCE RULES
RULE R1: ISOLATED(s) AND ENERGY_CONSERVATION_APPLIES(s) => Delta E_total(s) = 0.
RULE R2: CONSERVATIVE_FORCES_ONLY(s) => Delta(K + U) = 0.
RULE R3: WORK_NET(p) = w => Delta K(p) = w, for a particle in a Newtonian inertial frame.
RULE R4: ENERGY_TRANSFER(q, dt) AND dt > 0 => AVERAGE_POWER = q/dt.
RULE R5: ENERGY_VALUE(q, unit) AND unit compatible_with J => NORMALISE_TO_J(q).
RULE R6: SAME_SYSTEM_BOUNDARY_AND_CONVENTION(a,b) => COMPARABLE_ENERGY_ACCOUNTING(a,b).

21. INVALID INFERENCES
Energy is not synonymous with force, power, heat, temperature or matter.
No conservation conclusion without specifying system and external exchanges.
No claim that every isolated subsystem conserves its mechanical energy.
No universal identification of potential energy with a unique absolute value.

22. WORKED EXAMPLE: KINETIC ENERGY
Given m = 2 kg, v = 3 m/s:
E_k = (1/2)(2)(3^2) = 9 J.
If speed doubles to 6 m/s: E_k = 36 J.
Kinetic energy scales quadratically with speed in the nonrelativistic model.

23. WORKED EXAMPLE: GRAVITATIONAL POTENTIAL
Given m = 5 kg, g = 9.81 m/s^2, Delta h = 2 m:
Delta U = m g Delta h = 98.1 J.
Assumptions: approximately uniform gravitational field; negligible changes to g.

24. WORKED EXAMPLE: ELECTRICAL ENERGY
For constant electrical power P = 100 W over t = 60 s:
E = P t = 6000 J = 6 kJ.

25. WORKED EXAMPLE: FIRST LAW
Closed system receives Q = 500 J and performs W = 120 J.
Delta U = 500 - 120 = 380 J, ignoring changes in macroscopic kinetic and potential energy.

26. COMPUTATIONAL REPRESENTATION
EnergyRecord := {system_id, state_id, value, unit, frame?, reference_zero?, boundary?, model, timestamp?, uncertainty?, provenance?}.
Transformation := {input_states, output_states, transfer_terms, governing_equations, assumptions}.
Reject records with inconsistent units or missing required contextual fields.

27. VALIDATION
CHECK dimensional_consistency.
CHECK conservation_residual_within_uncertainty when conservation applies.
CHECK sign_conventions_documented.
CHECK reference_frame_compatible.
CHECK model_assumptions_declared.
CHECK uncertainty_and_provenance_recorded for empirical data.

28. SEMANTIC EQUIVALENCE
'Energetic content' is not automatically equivalent to thermodynamic internal energy.
'Heat energy' in informal prose maps to heat transfer only when a transfer process is described.
'Work' maps to energy transfer by generalised force-displacement interaction, not employment or computational workload.
'Power' maps to energy per unit time, not total energy.

29. CONFIDENCE
CONFIDENCE:
  formal_laws: high within explicitly stated models
  measured_values: dependent on calibration, uncertainty and evidence
  extrapolation: conditional on regime validity
  speculative_claims: do not promote to established physical laws

30. FLOW HASH
FLOW_HASH:
  algorithm: SHA-256
  input: canonical UTF-8 serialisation of ontology definitions, rules and version
  value: compute at publication time; not fabricated

31. UPDATE MODEL
UPDATE_MODEL:
  semantic_version: 1.1
  update_triggers: new validated evidence; changed definitions; corrections; revised standards
  preserve_provenance: true
  log_changes: true
  invalidate_dependent_inferences: when governing assumptions change

32. AI CONSUMPTION
AI_CONSUMPTION:
  entity_resolution: typed and context-sensitive
  unit_normalisation: SI
  reasoning: rule-based with explicit assumptions
  evidence_policy: source and uncertainty attached to empirical claims
  hallucination_guard: reject unsupported universal claims
  output: traceable propositions, equations and validation results

33. ONTOLOGY CONNECTIONS
Physical Entity Ontology -> HAS_PROPERTY -> Energy.
Matter Ontology -> HAS_REST_ENERGY -> Energy.
Force Ontology -> CAN_TRANSFER_BY_WORK -> Energy.
Thermodynamics Ontology -> ACCOUNTS_FOR -> Internal Energy.
Quantum Mechanics Ontology -> REPRESENTS_WITH -> Hamiltonian.
Measurement Ontology -> QUANTIFIES -> EnergyQuantity.

34. PROOF OBLIGATIONS
PO1: Any conservation claim specifies boundary and external exchanges.
PO2: Any numeric equation is dimensionally consistent.
PO3: Any comparison uses compatible reference conventions.
PO4: Any approximation states its regime.
PO5: Any empirical energy estimate includes provenance and uncertainty where available.

35. COMPLETION
END FLOW ALGEBRA