> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Calculate Clausius-Clapeyron Equation

> Calculates dP/dT along a phase transition curve using the Clausius-Clapeyron equation. This equation relates the slope of the coexistence curve to latent heat and volume change during a first-order phase transition. Applicable to modeling regime transitions and critical phenomena in markets.

**Use Cases:**
- Model phase transitions in market regimes
- Analyze critical phenomena and market crashes
- Study discontinuous transitions (e.g., liquidity crises)
- Regime change sensitivity analysis
- Thermodynamic analogies for market structure

**Formula:** dP/dT = ΔH / (T ΔV)

Where ΔH is latent heat and ΔV is volume change.

**Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE, Credits: 10]



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/thermodynamics/clausius-clapeyron
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Physics Module
  description: >-
    Physics and Information Theory module for FinceptQuantLib API. Includes
    Shannon/Renyi/Tsallis entropy, KL/JS divergence, mutual information,
    transfer entropy, Fisher information, Boltzmann distribution, Ising model,
    maximum entropy, thermodynamics (free energy, Carnot cycle, van der Waals
    equation), and Maxwell relations. **Pro Tier required. 5 credits per
    request.**
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-physics
    description: Physics and Information Theory module for FinceptQuantLib API
    x-displayName: Physics
paths:
  /quantlib/physics/thermodynamics/clausius-clapeyron:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Clausius-Clapeyron Equation
      description: >-
        Calculates dP/dT along a phase transition curve using the
        Clausius-Clapeyron equation. This equation relates the slope of the
        coexistence curve to latent heat and volume change during a first-order
        phase transition. Applicable to modeling regime transitions and critical
        phenomena in markets.


        **Use Cases:**

        - Model phase transitions in market regimes

        - Analyze critical phenomena and market crashes

        - Study discontinuous transitions (e.g., liquidity crises)

        - Regime change sensitivity analysis

        - Thermodynamic analogies for market structure


        **Formula:** dP/dT = ΔH / (T ΔV)


        Where ΔH is latent heat and ΔV is volume change.


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: clausius_clapeyron
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - delta_H
                - T
                - delta_V
              properties:
                delta_H:
                  type: number
                  description: >-
                    Latent heat (enthalpy change) during phase transition
                    (J/mol)
                  example: 40660
                T:
                  type: number
                  description: Temperature at phase transition (Kelvin)
                  example: 373.15
                delta_V:
                  type: number
                  description: Volume change during phase transition (m³/mol)
                  example: 0.03
            examples:
              water_vaporization:
                summary: Water vaporization at 100°C
                value:
                  delta_H: 40660
                  T: 373.15
                  delta_V: 0.03
              market_regime:
                summary: Market regime transition
                value:
                  delta_H: 1000
                  T: 300
                  delta_V: 0.1
      responses:
        '200':
          description: Clausius-Clapeyron equation calculated successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      dP_dT:
                        type: number
                        description: Slope of phase coexistence curve dP/dT (Pa/K)
                        example: 3631.8
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientCreditsError'
        '422':
          $ref: '#/components/responses/ValidationError'
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientCreditsError:
      description: Insufficient API credits
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Insufficient credits. This endpoint requires 5 credits.
    ValidationError:
      description: Request validation error
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: array
                items:
                  type: object
                  properties:
                    loc:
                      type: array
                      items:
                        type: string
                    msg:
                      type: string
                    type:
                      type: string
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````