> ## 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 Shannon Entropy

> Calculates the Shannon entropy of a discrete probability distribution, measuring the average information content or uncertainty. Shannon entropy is fundamental in information theory and is used to quantify the uncertainty in portfolio returns, market regimes, or trading signals. Higher entropy indicates greater uncertainty or diversity in outcomes.

**Use Cases:**
- Measure uncertainty in portfolio return distributions
- Quantify information content in market signals
- Assess diversity in asset allocations
- Evaluate predictability of financial time series
- Compare information efficiency across markets

**Formula:** H(X) = -Σ p(x) log(p(x))

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



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/entropy/shannon
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/shannon:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Shannon Entropy
      description: >-
        Calculates the Shannon entropy of a discrete probability distribution,
        measuring the average information content or uncertainty. Shannon
        entropy is fundamental in information theory and is used to quantify the
        uncertainty in portfolio returns, market regimes, or trading signals.
        Higher entropy indicates greater uncertainty or diversity in outcomes.


        **Use Cases:**

        - Measure uncertainty in portfolio return distributions

        - Quantify information content in market signals

        - Assess diversity in asset allocations

        - Evaluate predictability of financial time series

        - Compare information efficiency across markets


        **Formula:** H(X) = -Σ p(x) log(p(x))


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: shannon_entropy
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - probabilities
              properties:
                probabilities:
                  type: array
                  items:
                    type: number
                  description: Discrete probability distribution (must sum to 1)
                  example:
                    - 0.25
                    - 0.25
                    - 0.25
                    - 0.25
                base:
                  type: number
                  description: >-
                    Logarithm base for entropy calculation (e=2.718 for nats, 2
                    for bits, 10 for dits)
                  default: 2.718281828459045
                  example: 2.718281828459045
            examples:
              portfolio_states:
                summary: Portfolio state probabilities
                value:
                  probabilities:
                    - 0.4
                    - 0.3
                    - 0.2
                    - 0.1
                  base: 2.718281828459045
              uniform_distribution:
                summary: Maximum entropy (uniform distribution)
                value:
                  probabilities:
                    - 0.2
                    - 0.2
                    - 0.2
                    - 0.2
                    - 0.2
                  base: 2
      responses:
        '200':
          description: Shannon entropy calculated successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      shannon_entropy:
                        type: number
                        description: Shannon entropy value (higher = more uncertainty)
                        example: 1.2799
                      base:
                        type: number
                        description: Logarithm base used
                        example: 2.718281828459045
        '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

````