> ## 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.

# Get Maxwell Thermodynamic Relations

> Returns the four Maxwell relations, which are equalities between partial derivatives of thermodynamic potentials. These relations follow from the equality of mixed partial derivatives and connect different thermodynamic properties. Maxwell relations are fundamental in thermodynamics and have analogs in economic and financial theory.

**Use Cases:**
- Understand relationships between market variables
- Economic duality and reciprocity relations
- Theoretical constraints on model parameters
- Thermodynamic analogies in market microstructure
- Educational and reference purposes

**Maxwell Relations:**
1. (∂T/∂V)_S = -(∂P/∂S)_V
2. (∂T/∂P)_S = (∂V/∂S)_P
3. (∂S/∂V)_T = (∂P/∂T)_V
4. (∂S/∂P)_T = -(∂V/∂T)_P

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



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/thermodynamics/maxwell-relations
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/maxwell-relations:
    post:
      tags:
        - quantlib-physics
      summary: Get Maxwell Thermodynamic Relations
      description: >-
        Returns the four Maxwell relations, which are equalities between partial
        derivatives of thermodynamic potentials. These relations follow from the
        equality of mixed partial derivatives and connect different
        thermodynamic properties. Maxwell relations are fundamental in
        thermodynamics and have analogs in economic and financial theory.


        **Use Cases:**

        - Understand relationships between market variables

        - Economic duality and reciprocity relations

        - Theoretical constraints on model parameters

        - Thermodynamic analogies in market microstructure

        - Educational and reference purposes


        **Maxwell Relations:**

        1. (∂T/∂V)_S = -(∂P/∂S)_V

        2. (∂T/∂P)_S = (∂V/∂S)_P

        3. (∂S/∂V)_T = (∂P/∂T)_V

        4. (∂S/∂P)_T = -(∂V/∂T)_P


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: maxwell_relations
      requestBody:
        required: false
        content:
          application/json:
            schema:
              type: object
              properties: {}
      responses:
        '200':
          description: Maxwell relations returned successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      maxwell_relations:
                        type: array
                        items:
                          type: string
                        description: List of Maxwell relations
                        example:
                          - (∂T/∂V)_S = -(∂P/∂S)_V
                          - (∂T/∂P)_S = (∂V/∂S)_P
                          - (∂S/∂V)_T = (∂P/∂T)_V
                          - (∂S/∂P)_T = -(∂V/∂T)_P
        '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

````