> ## 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 Differential Entropy

> Calculates the differential entropy for continuous probability distributions (Gaussian or exponential). Differential entropy extends the concept of entropy to continuous random variables and can be negative (unlike discrete entropy). Essential for continuous financial models, option pricing, and Bayesian inference.

**Use Cases:**
- Measure uncertainty in continuous return distributions
- Information content in continuous signals
- Gaussian process modeling
- Entropy of volatility distributions
- Continuous-time information theory

**Formulas:**
- Gaussian: h(X) = 0.5 log(2πe σ²)
- Exponential: h(X) = 1 + log(λ⁻¹)

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



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/entropy/differential
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/entropy/differential:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Differential Entropy
      description: >-
        Calculates the differential entropy for continuous probability
        distributions (Gaussian or exponential). Differential entropy extends
        the concept of entropy to continuous random variables and can be
        negative (unlike discrete entropy). Essential for continuous financial
        models, option pricing, and Bayesian inference.


        **Use Cases:**

        - Measure uncertainty in continuous return distributions

        - Information content in continuous signals

        - Gaussian process modeling

        - Entropy of volatility distributions

        - Continuous-time information theory


        **Formulas:**

        - Gaussian: h(X) = 0.5 log(2πe σ²)

        - Exponential: h(X) = 1 + log(λ⁻¹)


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: differential_entropy
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              properties:
                distribution:
                  type: string
                  enum:
                    - gaussian
                    - exponential
                  description: Type of continuous distribution
                  default: gaussian
                  example: gaussian
                sigma:
                  type: number
                  description: Standard deviation (for Gaussian distribution)
                  default: 1
                  example: 0.2
                rate:
                  type: number
                  description: Rate parameter λ (for exponential distribution)
                  default: 1
                  example: 0.5
            examples:
              return_distribution:
                summary: Daily return distribution (Gaussian)
                value:
                  distribution: gaussian
                  sigma: 0.015
              waiting_time:
                summary: Waiting time (exponential)
                value:
                  distribution: exponential
                  rate: 0.1
      responses:
        '200':
          description: Differential entropy calculated successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      differential_entropy:
                        type: number
                        description: >-
                          Differential entropy (can be negative for narrow
                          distributions)
                        example: -2.8327
                      distribution:
                        type: string
                        description: Distribution type used
                        example: gaussian
        '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

````