Entropy Measurement Ontology

# Entropy Measurement Ontology — Flow Algebra

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

FLOW EntropyMeasurementOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Thermal Measurements
    -> Entropy Measurement Ontology

  PURPOSE:
    Represent entropy measurement and inference as the quantitative determination of entropy, entropy change, specific entropy, molar entropy, entropy transfer, and entropy generation from thermodynamic state data, reversible heat-transfer relationships, calorimetric measurements, equations of state, and process models, including units, reference states, uncertainty, irreversibility, and distinctions from heat, energy and temperature.

  ENTITY Entropy {
    TYPE: ThermodynamicStateQuantity
    SYMBOL: S
    DIMENSION: M * L^2 * T^-2 * Theta^-1
    SI_UNIT: joule_per_kelvin
    SI_SYMBOL: J/K

    REVERSIBLE_DIFFERENTIAL_RELATION:
      dS = delta_Q_rev/T

    PROPERTIES:
      is_scalar
      is_extensive
      is_state_function
      has_value
      has_unit
      has_dimension
      may_require_reference_state_for_absolute_tabulation
      may_be_transferred
      may_be_generated
      may_have_uncertainty
  }

  ENTITY EntropyChange {
    TYPE: ThermodynamicStateDifference
    SYMBOL: delta_S
    SI_UNIT: joule_per_kelvin
    SI_SYMBOL: J/K

    DEFINITION:
      delta_S = S_2 - S_1
  }

  ENTITY SpecificEntropy {
    TYPE: IntensiveThermodynamicQuantity
    SYMBOL: s
    SI_UNIT: joule_per_kilogram_kelvin
    SI_SYMBOL: J/(kg*K)

    RELATION:
      s = S/m
      WHEN m != 0
  }

  ENTITY MolarEntropy {
    TYPE: MolarThermodynamicQuantity
    SYMBOL: S_m
    SI_UNIT: joule_per_mole_kelvin
    SI_SYMBOL: J/(mol*K)

    RELATION:
      S_m = S/n
      WHEN n != 0
  }

  ENTITY EntropyGeneration {
    TYPE: IrreversibilityQuantity
    SYMBOL: S_gen
    SI_UNIT: joule_per_kelvin
    SI_SYMBOL: J/K

    CONSTRAINT:
      S_gen >= 0
      FOR real_processes_under_standard_classical_thermodynamic_interpretation
  }

  UNIT_SYSTEM {
    TOTAL_ENTROPY:
      canonical_unit: joule_per_kelvin
      symbol: J/K

    SPECIFIC_ENTROPY:
      canonical_unit: joule_per_kilogram_kelvin
      symbol: J/(kg*K)

    MOLAR_ENTROPY:
      canonical_unit: joule_per_mole_kelvin
      symbol: J/(mol*K)

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

  CLASSIFICATION {
    by basis:
      total_entropy
      specific_entropy
      molar_entropy

    by process role:
      entropy_change
      entropy_transfer
      entropy_generation

    by measurement inference:
      calorimetric_entropy
      state_function_entropy
      statistical_entropy
      process_entropy_balance
  }

  STATE_FUNCTION_MODEL {
    PROPERTY:
      entropy_is_state_function = true

    CONSEQUENCE:
      delta_S depends_only_on_initial_and_final_equilibrium_states

    PATH:
      actual_process_path MAY be irreversible
      while_entropy_change_can_be_computed_using_any_convenient_reversible_path
      between_same_states

    RULE:
      entropy_change MUST_NOT be confused_with_entropy_generation
  }

  REVERSIBLE_HEAT_MODEL {
    DIFFERENTIAL:
      dS = delta_Q_rev/T

    FINITE:
      delta_S = integral(delta_Q_rev/T)

    ISOTHERMAL_REVERSIBLE:
      delta_S = Q_rev/T
      WHEN T_constant_and_T > 0

    RULE:
      actual_irreversible_heat Q
      MUST_NOT automatically_be_substituted_for delta_Q_rev
      in_state_entropy_integral
  }

  CLAUSIUS_MODEL {
    REVERSIBLE_CYCLE:
      closed_integral(delta_Q_rev/T) = 0

    IRREVERSIBLE_CYCLE:
      closed_integral(delta_Q/T) < 0
      under_standard_sign_convention_for_heat_into_system

    CLAUSIUS_INEQUALITY:
      closed_integral(delta_Q/T) <= 0

    RULE:
      sign_convention_and_boundary_temperature
      MUST be preserved
  }

  ENTROPY_BALANCE_MODEL {
    CLOSED_SYSTEM:
      delta_S_system =
        integral(delta_Q_boundary/T_boundary)
        + S_gen

    CONSTRAINT:
      S_gen >= 0

    ISOLATED_SYSTEM:
      delta_S_system = S_gen >= 0

    REVERSIBLE_PROCESS:
      S_gen = 0

    IRREVERSIBLE_PROCESS:
      S_gen > 0

    RULE:
      entropy_transfer_and_entropy_generation
      MUST be separately_accounted
  }

  OPEN_SYSTEM_MODEL {
    CONTROL_VOLUME_RATE_BALANCE:
      dS_cv/dt =
        sum(m_dot_in*s_in)
        - sum(m_dot_out*s_out)
        + sum(Q_dot_j/T_j)
        + S_dot_gen

    STEADY_STATE:
      dS_cv/dt = 0

    CONSTRAINT:
      S_dot_gen >= 0

    REQUIRE:
      mass_flow_rates
      specific_entropies
      boundary_heat_transfer_rates
      boundary_temperatures
      system_boundary
  }

  CALORIMETRIC_MODEL {
    CONSTANT_PRESSURE_HEAT_CAPACITY:
      delta_S =
        integral_T1_to_T2(C_p(T)/T dT)
      FOR appropriate_constant_pressure_reference_path

    CONSTANT_VOLUME_HEAT_CAPACITY:
      delta_S =
        integral_T1_to_T2(C_v(T)/T dT)
      FOR appropriate_constant_volume_reference_path

    PHASE_TRANSITION:
      delta_S_transition =
        delta_H_transition/T_transition
      FOR reversible_equilibrium_transition

    REQUIRE:
      absolute_temperature_in_kelvin
      valid_heat_capacity_data
      phase_transition_data_when_crossed
  }

  IDEAL_GAS_MODEL {
    MOLAR_FORM:
      delta_s_molar =
        C_p_molar*ln(T_2/T_1)
        - R*ln(p_2/p_1)
      WHEN C_p_molar_constant_approximation

    ALTERNATIVE:
      delta_s_molar =
        C_v_molar*ln(T_2/T_1)
        + R*ln(v_2/v_1)

    REQUIRE:
      positive_absolute_temperatures
      positive_pressures_or_specific_volumes
      ideal_gas_context

    RULE:
      logarithm_arguments MUST be dimensionless_ratios
  }

  STATISTICAL_MODEL {
    BOLTZMANN_RELATION:
      S = k_B*ln(Omega)

    WHERE:
      k_B = Boltzmann_constant
      Omega = number_of_accessible_microstates

    GIBBS_FORM:
      S = -k_B*sum(p_i*ln(p_i))

    RULE:
      thermodynamic_and_statistical_entropy
      are_related_but_require_defined_ensemble_and_state_semantics
  }

  THIRD_LAW_REFERENCE_MODEL {
    IDEAL_PERFECT_CRYSTAL:
      S -> 0
      as T -> 0 K
      under idealised_third_law_conditions

    ABSOLUTE_ENTROPY:
      may_be_constructed_by_integrating_heat_capacity_over_temperature
      and_adding_phase_transition_entropy_changes

    RULE:
      residual_entropy_or_degeneracy
      requires_explicit_material_state_context
  }

  IRREVERSIBILITY_MODEL {
    entropy_generation_sources:
      heat_transfer_across_finite_temperature_difference
      friction
      viscous_dissipation
      mixing
      diffusion
      chemical_reaction
      electrical_resistance
      inelastic_deformation

    RULE:
      entropy_generation_is_nonnegative
      but_local_entropy_flux_and_system_entropy_change_may_have_either_sign
      depending_on_open_system_exchange
  }

  RELATIONSHIPS {
    Entropy -> HAS_DIMENSION -> M*L^2*T^-2*Theta^-1
    Entropy -> MEASURED_IN -> JoulePerKelvin
    Entropy -> IS -> StateFunction
    EntropyChange -> DIFFERENCE_OF -> EntropyStates
    ReversibleHeatTransfer -> RELATES_TO -> EntropyChangeAndTemperature
    EntropyGeneration -> MEASURES -> Irreversibility
    SpecificEntropy -> ENTROPY_PER -> Mass
    MolarEntropy -> ENTROPY_PER -> AmountOfSubstance
    HeatCapacity -> CONTRIBUTES_TO -> CalorimetricEntropyChange
    PhaseTransition -> CONTRIBUTES_TO -> EntropyChange
    EntropyBalance -> COMBINES -> TransferAndGeneration
  }

  SEMANTIC_EQUIVALENCE {
    "entropy measurement" ~= entropy_determination
    "J/K" ~= joule_per_kelvin
    "specific entropy" ~= entropy_per_unit_mass
    "molar entropy" ~= entropy_per_mole

    entropy != heat
    entropy != temperature
    entropy != internal_energy
    entropy_change != entropy_generation
    entropy_transfer != entropy_generation
    entropy != disorder_as_complete_definition
  }

  CONSTRAINTS {
    entropy_is_state_function = true
    entropy_is_extensive = true
    specific_entropy_is_intensive = true
    dimensional_formula = M*L^2*T^-2*Theta^-1
    SI_unit = J/K
    absolute_temperature_in_entropy_integrals_must_use_kelvin = true
    entropy_generation_must_be_nonnegative_for_real_processes = true
    entropy_change_and_entropy_generation_are_not_semantically_equivalent = true
    reversible_heat_relation_requires_reversible_path_or_equivalent_state_calculation = true
    system_boundary_and_sign_convention_must_be_preserved = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      Entropy
      EntropyChange
      SpecificEntropy
      MolarEntropy
      EntropyGeneration

    COMMON_METHODS:
      calorimetric_inference
      equation_of_state_inference
      thermodynamic_property_table_inference
      phase_transition_measurement
      process_entropy_balance
      statistical_mechanical_inference

    INSTRUMENTS_AND_DATA:
      calorimeter
      differential_scanning_calorimeter
      temperature_sensor
      pressure_sensor
      mass_flow_meter
      heat_flux_sensor
      equation_of_state_data
      reference_property_database

    RECORD:
      entropy_quantity_type
      numerical_value
      unit
      total_specific_or_molar_basis
      initial_state
      final_state
      temperature
      pressure
      volume_or_density
      material
      composition
      phase
      system_boundary
      heat_transfer
      boundary_temperature
      mass_flow_when_relevant
      reference_state
      measurement_or_inference_method
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_entropy_quantity = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF initial_entropy_and_final_entropy_known
      THEN entropy_change = final_entropy - initial_entropy

    IF reversible_heat_path_known AND absolute_temperature_known
      THEN entropy_change =
        integral(reversible_heat_increment/temperature)

    IF reversible_isothermal_heat_known AND temperature > 0
      THEN entropy_change = reversible_heat/temperature

    IF heat_capacity_function_known AND valid_reversible_heating_path
      THEN entropy_change =
        integral(heat_capacity(T)/T dT)

    IF reversible_phase_transition_enthalpy_known
      AND transition_temperature > 0
      THEN transition_entropy =
        transition_enthalpy/transition_temperature

    IF closed_system_entropy_change_and_entropy_transfer_known
      THEN entropy_generation =
        entropy_change - entropy_transfer

    IF system_is_isolated
      THEN entropy_change = entropy_generation
      AND entropy_change >= 0

    IF process_is_reversible
      THEN entropy_generation = 0

    IF ideal_gas_states_known
      THEN infer_entropy_change
      using_valid_ideal_gas_relation
  }

  REFERENCE_STATE_MODEL {
    entropy_difference:
      independent_of_arbitrary_common_reference_offset

    absolute_tabulated_entropy:
      requires_defined_reference_convention_or_third_law_construction

    property_tables:
      may_use_reference_state_specific_to_dataset

    RULE:
      entropy_values_from_different_reference_conventions
      MUST be aligned_before_direct_comparison
  }

  SYSTEM_BOUNDARY_MODEL {
    REQUIRE:
      system_or_control_volume
      surroundings
      heat_transfer_boundaries
      boundary_temperatures
      mass_transfer_when_open
      sign_convention

    RULE:
      entropy_balance_without_boundary_definition
      is_semantically_incomplete
  }

  UNCERTAINTY_MODEL {
    sources:
      temperature_measurement
      pressure_measurement
      heat_measurement
      heat_capacity_data
      phase_transition_enthalpy
      mass_or_amount
      mass_flow
      boundary_temperature
      equation_of_state
      reference_state
      numerical_integration
      calibration
      model_assumptions

    PROPAGATION:
      derived_entropy_uncertainty
      <- thermodynamic_state_measurement_and_model_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    second_law_relationship_confidence: 1.00
    calorimetric_relationship_confidence: 0.99
    measurement_context_confidence: 0.97

    RULE:
      confidence decreases when state variables, process constraint,
      system boundary, reference state, phase data,
      boundary temperature, calibration or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK total_specific_or_molar_basis
    CHECK absolute_temperature_in_kelvin
    CHECK initial_and_final_states
    CHECK entropy_change_vs_generation
    CHECK reversible_vs_irreversible_context
    CHECK system_boundary
    CHECK sign_convention
    CHECK reference_state
    CHECK phase_transition_terms
    CHECK heat_capacity_data_range
    CHECK ideal_gas_assumptions_when_used
    CHECK nonnegative_entropy_generation
    CHECK calibration_and_data_provenance
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement_or_inference:
      identify_entropy_quantity_type
      validate_unit
      identify_total_specific_or_molar_basis
      attach_initial_and_final_states
      attach_temperature_pressure_and_volume_context
      identify_material_composition_and_phase
      identify_system_boundary
      identify_reference_state
      identify_measurement_or_inference_method
      normalize_to_canonical_SI_basis
      preserve_original_value_and_unit
      attach_uncertainty
      update_entropy_state

    ON process_update:
      update_heat_transfer
      update_boundary_temperature
      update_mass_transfer
      recompute_entropy_transfer
      recompute_entropy_generation
      verify_second_law_constraint

    ON phase_change:
      attach_transition_temperature
      attach_transition_enthalpy
      compute_transition_entropy_when_valid
      preserve_phase_provenance

    ON reference_state_change:
      preserve_entropy_differences
      transform_reference_dependent_absolute_values
      record_reference_revision

    ON calibration_revision:
      preserve_provenance
      recompute_affected_inferences
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Entropy
    canonical_symbol: S
    canonical_dimension: M*L^2*T^-2*Theta^-1
    canonical_SI_unit: J/K

    interpretation_order:
      identify_entropy_quantity
      identify_value
      identify_unit
      identify_total_specific_or_molar_basis
      identify_initial_and_final_states
      identify_temperature_pressure_volume_and_phase
      identify_reversible_or_irreversible_context
      identify_heat_transfer_and_boundary_temperature
      identify_system_boundary
      identify_mass_transfer_for_open_system
      identify_reference_state
      identify_measurement_or_inference_method
      identify_uncertainty
      normalize_units
      validate_second_law_constraints
      infer_entropy_relationships

    ambiguity_controls:
      distinguish_entropy_from_heat
      distinguish_entropy_from_temperature
      distinguish_entropy_from_internal_energy
      distinguish_entropy_change_from_entropy_generation
      distinguish_entropy_transfer_from_entropy_generation
      distinguish_total_from_specific_and_molar_entropy
      distinguish_reversible_heat_relation_from_actual_irreversible_heat
      distinguish_thermodynamic_entropy_from_informal_disorder_language
      preserve_system_boundary_reference_state_and_sign_convention
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_thermal_entropy_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Thermal Measurements
      -> Entropy Measurement Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      state_function_model
      reversible_heat_model
      Clausius_model
      entropy_balance_model
      open_system_model
      calorimetric_model
      ideal_gas_model
      statistical_model
      third_law_reference_model
      irreversibility_model
      reference_state_model
      system_boundary_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      entropy_balance_model_changes
      reversible_or_irreversible_model_changes
      calorimetric_model_changes
      equation_of_state_model_changes
      reference_state_model_changes
      measurement_model_changes
      system_boundary_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW