Energy Ontology

# Energy Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/mechanical-measurements/energy-ontology.html

FLOW EnergyOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Mechanical Measurements
    -> Energy Ontology

  PURPOSE:
    Represent energy as a measurable scalar physical quantity associated with the state, motion, configuration, interactions, and capacity for physical change of a system, including mechanical energy, kinetic energy, potential energy, work, transfer, conservation, units, dimensional structure, reference states, measurement conditions, uncertainty, and relationships to force, displacement, power and momentum.

  ENTITY Energy {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: E
    DIMENSION: M * L^2 * T^-2
    SI_UNIT: joule
    SI_SYMBOL: J

    GENERAL_DEFINITION:
      energy := scalar_physical_quantity_associated_with_system_state_and_transfer

    PROPERTIES:
      is_scalar
      has_value
      has_unit
      has_dimension
      may_be_stored
      may_be_transferred
      may_be_transformed
      may_be_conserved
      may_require_reference_state
      may_have_uncertainty
  }

  ENTITY Work {
    TYPE: EnergyTransferQuantity
    SYMBOL: W
    DIMENSION: M * L^2 * T^-2
    SI_UNIT: joule
    SI_SYMBOL: J

    DEFINITION:
      work := integral_along_path(Force dot Displacement)

    DIFFERENTIAL_FORM:
      dW = F dot dr

    CONSTANT_FORCE_FORM:
      W = F * s * cos(theta)

    RELATION:
      Work -> TRANSFERS -> Energy
  }

  ENTITY KineticEnergy {
    TYPE: MechanicalEnergy
    SYMBOL: K

    CLASSICAL_FORM:
      K = 0.5 * m * v^2

    MOMENTUM_FORM:
      K = p^2 / (2*m)
      WHEN classical_nonrelativistic_context AND m != 0
  }

  ENTITY PotentialEnergy {
    TYPE: MechanicalEnergy
    SYMBOL: U

    DEFINITION:
      energy_associated_with_configuration_in_conservative_interaction

    RELATION:
      conservative_force = -gradient(PotentialEnergy)

    REFERENCE_RULE:
      absolute_zero_level_may_be_chosen_by_convention
      while_energy_differences_remain_physically_relevant
  }

  ENTITY MechanicalEnergy {
    TYPE: EnergyAggregate
    SYMBOL: E_mech

    FORM:
      E_mech = KineticEnergy + PotentialEnergy
  }

  ENTITY Power {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: P
    DIMENSION: M * L^2 * T^-3
    SI_UNIT: watt
    SI_SYMBOL: W

    RELATION:
      Power = rate_of_change(Energy, Time)

    FORM:
      P = dE/dt
  }

  ENTITY Force {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: F
    DIMENSION: M * L * T^-2

    RELATION:
      Force dot Displacement -> Work
  }

  ENTITY Momentum {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: p
    DIMENSION: M * L * T^-1

    RELATION:
      classical_kinetic_energy = p^2/(2*m)
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: joule
      symbol: J

      equivalence:
        1 J = 1 N*m
        1 J = 1 kg*m^2/s^2
    }

    COMMON_ALTERNATIVES {
      kilojoule
      megajoule
      watt_hour
      kilowatt_hour
      calorie
      kilocalorie
      electronvolt
      foot_pound_force
    }

    SEMANTIC_UNIT_RULE:
      joule_for_energy MUST_REMAIN_SEMANTICALLY_DISTINCT_FROM newton_metre_as_torque
      DESPITE identical_base_dimensions

    CONVERSION_RULE:
      energy_value(target_unit)
        = energy_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    mechanical:
      kinetic_energy
      gravitational_potential_energy
      elastic_potential_energy
      mechanical_energy

    broader_physical_forms:
      thermal_energy
      chemical_energy
      electrical_energy
      electromagnetic_energy
      nuclear_energy
      internal_energy
      rest_energy

    by_system_role:
      stored_energy
      transferred_energy
      dissipated_energy
      conserved_total_energy
  }

  RELATIONSHIPS {
    Energy -> HAS_DIMENSION -> M*L^2*T^-2
    Energy -> MEASURED_IN -> Joule
    Work -> TRANSFERS -> Energy
    Power -> RATE_OF_ENERGY_TRANSFER -> Energy
    KineticEnergy -> DEPENDS_ON -> Mass
    KineticEnergy -> DEPENDS_ON -> Velocity
    PotentialEnergy -> DEPENDS_ON -> Configuration
    ConservativeForce -> RELATED_TO -> PotentialEnergyGradient
    MechanicalEnergy -> SUM_OF -> KineticEnergy
    MechanicalEnergy -> SUM_OF -> PotentialEnergy
    ClosedSystem -> CONSERVES -> TotalEnergy
  }

  SEMANTIC_EQUIVALENCE {
    "joule" ~= "J"
    "newton metre" ~= "joule" WHEN energy_or_work_context
    "kg m squared per second squared" ~= "J"
    work ~= energy_transfer
    energy != power
    energy != force
    energy != momentum
    energy != torque
    kinetic_energy != momentum
  }

  CONSERVATION_MODEL {
    PRINCIPLE:
      total_energy_of_isolated_system = constant

    TRANSFORMATION:
      energy_form_A -> energy_form_B
      WITHOUT creation_or_destruction_of_total_energy

    OPEN_SYSTEM:
      change_in_system_energy
        = energy_transferred_into_system
        - energy_transferred_out_of_system
        + internally_accounted_source_terms_if_model_requires

    MECHANICAL_CONSERVATION:
      IF only_conservative_forces_do_work
      THEN K + U = constant
  }

  WORK_ENERGY_MODEL {
    WORK_ENERGY_THEOREM:
      net_work = change_in_kinetic_energy

    FORM:
      W_net = delta_K

    GENERAL_WORK:
      W = integral(F dot dr)

    RULE:
      force_perpendicular_to_displacement
      -> instantaneous_work_contribution = 0
  }

  KINETIC_ENERGY_MODEL {
    CLASSICAL:
      K = 0.5*m*v^2

    CONDITIONS:
      classical_mechanics
      nonrelativistic_speed
      mass_defined

    PROPERTIES:
      K >= 0
      for_positive_mass_classical_particle

    RULE:
      doubling_speed -> quadruples_kinetic_energy
      WHEN mass_constant
  }

  POTENTIAL_ENERGY_MODEL {
    CONSERVATIVE_FORCE_RELATION:
      F = -grad(U)

    ONE_DIMENSION:
      F_x = -dU/dx

    GRAVITATIONAL_NEAR_EARTH:
      delta_U = m*g*delta_h
      WHEN uniform_gravitational_field_approximation

    ELASTIC_SPRING:
      U = 0.5*k*x^2
      WHEN ideal_Hookean_spring

    REFERENCE:
      potential_energy_zero_level_must_be_defined_or_understood
  }

  CONSTRAINTS {
    energy_is_scalar_quantity = true
    dimensional_formula = M*L^2*T^-2
    SI_unit = J
    total_energy_conservation_requires_defined_system_boundary = true
    mechanical_energy_conservation_requires_applicable_force_conditions = true
    potential_energy_values_may_depend_on_reference_zero = true
    energy_and_power_are_not_semantically_equivalent = true
    energy_and_torque_are_not_semantically_equivalent = true
    identical_dimensions_do_not_guarantee_semantic_equivalence = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Energy

    DIRECT_OR_INFERRED_CONTEXT:
      calorimetry
      electrical_energy_metering
      mechanical_work_measurement
      kinetic_state_inference
      potential_state_inference

    INDIRECT_MEASUREMENT:
      force_displacement_integration
      power_time_integration
      mass_velocity_relation
      state_function_difference
      thermal_or_electrical_measurement_models

    RECORD:
      numerical_value
      unit
      energy_type
      system_boundary
      initial_state
      final_state
      reference_state
      timestamp
      measurement_method
      instrument
      calibration_state
      uncertainty
      environmental_conditions

    UNCERTAINTY:
      measured_or_inferred_energy = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF mass_known AND speed_known AND classical_conditions_apply
      THEN kinetic_energy = 0.5 * mass * speed^2

    IF net_work_known
      THEN kinetic_energy_change = net_work

    IF force_and_path_known
      THEN work = integral_along_path(force dot displacement)

    IF power_known_as_function_of_time
      THEN transferred_energy = integral(power, time)

    IF constant_power AND time_interval_known
      THEN transferred_energy = power * time_interval

    IF only_conservative_forces_act
      THEN mechanical_energy = kinetic_energy + potential_energy = constant

    IF isolated_system
      THEN total_energy_before = total_energy_after

    IF potential_energy_function_known
      THEN conservative_force = -gradient(potential_energy)

    IF energy_change_known AND time_interval_known AND time_interval != 0
      THEN average_power = energy_change / time_interval
  }

  SYSTEM_BOUNDARY_MODEL {
    REQUIRE:
      define_system
      identify_surroundings
      identify_energy_crossing_boundary
      identify_internal_energy_transformations

    TRANSFER_MODES:
      work
      heat
      matter_transfer
      radiation
      electrical_transfer

    RULE:
      conservation_statement MUST specify system_boundary_and_accounting_scope
  }

  REFERENCE_STATE_MODEL {
    relevant_for:
      potential_energy
      internal_energy_differences
      other_state_dependent_energy_descriptions

    RULE:
      energy_difference MAY_BE physically meaningful
      even_when_absolute_reference_is_conventional

    REQUIRE:
      preserve_reference_state_when_comparing_values
  }

  ENERGY_POWER_MODEL {
    instantaneous_power:
      P = dE/dt

    average_power:
      P_avg = delta_E / delta_t

    mechanical_power:
      P = F dot v
      WHEN force_velocity_context

    rotational_power:
      P = tau dot omega
      WHEN rotational_mechanics_context
  }

  TORQUE_ENERGY_DISTINCTION {
    energy_unit:
      J

    torque_unit:
      N*m

    dimensional_equivalence:
      dimension(Energy) = dimension(Torque)

    semantic_distinction:
      Energy is scalar state_or_transfer quantity
      Torque is rotational vector_or_pseudovector tendency

    RULE:
      DO_NOT infer semantic_equivalence_from_identical_dimensions
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    conservation_relationship_confidence: 1.00
    mechanical_relationship_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when energy type, unit, system boundary,
      reference state, transfer mechanism, measurement method,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK energy_type
    CHECK system_boundary_for_conservation_claim
    CHECK reference_state_when_required
    CHECK conservative_force_conditions_for_mechanical_energy_conservation
    CHECK classical_conditions_for_kinetic_energy_formula
    CHECK torque_energy_semantic_distinction
    CHECK power_energy_semantic_distinction
    CHECK instrument_calibration_when_measured
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_energy_type
      identify_system_boundary
      identify_reference_state_when_required
      normalize_to_canonical_unit
      preserve_original_value_and_unit
      attach_timestamp
      attach_uncertainty
      update_energy_state

    ON energy_transfer_event:
      identify_transfer_mode
      identify_source_and_destination
      record_initial_energy_state
      record_transferred_energy
      record_final_energy_state
      test_conservation_balance
      preserve_event_provenance

    ON reference_state_change:
      preserve_energy_differences
      recompute_reference_dependent_values
      record_reference_revision

    ON revised_calibration:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Energy
    canonical_symbol: E
    canonical_dimension: M*L^2*T^-2
    canonical_SI_unit: J

    interpretation_order:
      identify_quantity
      identify_energy_type
      identify_value
      identify_unit
      identify_system_boundary
      identify_initial_and_final_states
      identify_reference_state
      identify_transfer_or_transformation
      identify_force_displacement_or_power_time_context
      identify_measurement_method
      identify_uncertainty
      validate_dimensions
      infer_conservation_relationships

    ambiguity_controls:
      distinguish_energy_from_power
      distinguish_energy_from_force
      distinguish_energy_from_momentum
      distinguish_energy_from_torque
      distinguish_stored_energy_from_energy_transfer
      distinguish_kinetic_from_potential_energy
      distinguish_total_energy_from_mechanical_energy
      distinguish_absolute_value_from_reference_dependent_energy
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_mechanical_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Mechanical Measurements
      -> Energy Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      conservation_model
      work_energy_model
      kinetic_energy_model
      potential_energy_model
      system_boundary_model
      reference_state_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      conservation_model_changes
      reference_state_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW