> ## 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 Carnot Cycle Properties

> Calculates properties of an ideal Carnot heat engine cycle operating between hot and cold reservoirs. Returns maximum theoretical efficiency, work output per cycle, heat rejected, and coefficients of performance for refrigerator and heat pump modes. The Carnot efficiency sets fundamental limits on energy conversion efficiency.

**Use Cases:**
- Theoretical efficiency bounds for financial engines
- Information-to-profit conversion limits
- Market maker efficiency analysis
- Energy/work analogies in portfolio rebalancing
- Maximum extractable value calculations

**Formula:** η_Carnot = 1 - T_cold/T_hot (maximum efficiency)

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



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/thermodynamics/carnot
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/carnot:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Carnot Cycle Properties
      description: >-
        Calculates properties of an ideal Carnot heat engine cycle operating
        between hot and cold reservoirs. Returns maximum theoretical efficiency,
        work output per cycle, heat rejected, and coefficients of performance
        for refrigerator and heat pump modes. The Carnot efficiency sets
        fundamental limits on energy conversion efficiency.


        **Use Cases:**

        - Theoretical efficiency bounds for financial engines

        - Information-to-profit conversion limits

        - Market maker efficiency analysis

        - Energy/work analogies in portfolio rebalancing

        - Maximum extractable value calculations


        **Formula:** η_Carnot = 1 - T_cold/T_hot (maximum efficiency)


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: carnot_cycle
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - T_hot
                - T_cold
              properties:
                T_hot:
                  type: number
                  description: >-
                    Hot reservoir temperature (absolute temperature, e.g.,
                    Kelvin)
                  example: 500
                T_cold:
                  type: number
                  description: >-
                    Cold reservoir temperature (absolute temperature, must be
                    less than T_hot)
                  example: 300
                Q_hot:
                  type: number
                  description: Heat absorbed from hot reservoir per cycle
                  default: 1000
                  example: 1000
            examples:
              typical_engine:
                summary: Typical heat engine
                value:
                  T_hot: 600
                  T_cold: 300
                  Q_hot: 1000
              small_difference:
                summary: Small temperature difference
                value:
                  T_hot: 320
                  T_cold: 300
                  Q_hot: 500
      responses:
        '200':
          description: Carnot cycle properties calculated successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      efficiency:
                        type: number
                        description: Carnot efficiency (0 to 1)
                        example: 0.5
                      work_per_cycle:
                        type: number
                        description: Work output per cycle W = η * Q_hot
                        example: 500
                      heat_rejected:
                        type: number
                        description: Heat rejected to cold reservoir Q_cold = Q_hot - W
                        example: 500
                      cop_refrigerator:
                        type: number
                        description: Coefficient of performance as refrigerator
                        example: 1
                      cop_heat_pump:
                        type: number
                        description: Coefficient of performance as heat pump
                        example: 2
        '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

````