> ## 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 Tsallis Entropy

> Calculates the Tsallis entropy, a non-extensive generalization of Shannon entropy parameterized by q. Particularly useful for systems with long-range correlations, power-law distributions, and non-equilibrium states common in financial markets. q=1 recovers Shannon entropy.

**Use Cases:**
- Analyze fat-tailed return distributions
- Model markets with long-range correlations
- Study non-equilibrium market dynamics
- Measure complexity in fractal market structures
- Assess systemic risk in interconnected systems

**Formula:** S_q(X) = (1 - Σ p(x)^q) / (q - 1)

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



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/entropy/tsallis
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/tsallis:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Tsallis Entropy
      description: >-
        Calculates the Tsallis entropy, a non-extensive generalization of
        Shannon entropy parameterized by q. Particularly useful for systems with
        long-range correlations, power-law distributions, and non-equilibrium
        states common in financial markets. q=1 recovers Shannon entropy.


        **Use Cases:**

        - Analyze fat-tailed return distributions

        - Model markets with long-range correlations

        - Study non-equilibrium market dynamics

        - Measure complexity in fractal market structures

        - Assess systemic risk in interconnected systems


        **Formula:** S_q(X) = (1 - Σ p(x)^q) / (q - 1)


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: tsallis_entropy
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - probabilities
                - q
              properties:
                probabilities:
                  type: array
                  items:
                    type: number
                  description: Discrete probability distribution (must sum to 1)
                  example:
                    - 0.5
                    - 0.3
                    - 0.15
                    - 0.05
                q:
                  type: number
                  description: >-
                    Tsallis parameter (q<1: super-extensive, q=1: Shannon
                    entropy, q>1: sub-extensive)
                  example: 1.5
            examples:
              fat_tailed:
                summary: Fat-tailed distribution analysis
                value:
                  probabilities:
                    - 0.7
                    - 0.15
                    - 0.1
                    - 0.05
                  q: 1.5
              near_shannon:
                summary: Near Shannon entropy
                value:
                  probabilities:
                    - 0.25
                    - 0.25
                    - 0.25
                    - 0.25
                  q: 1.01
      responses:
        '200':
          description: Tsallis entropy calculated successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      tsallis_entropy:
                        type: number
                        description: Tsallis entropy value
                        example: 0.7845
                      q:
                        type: number
                        description: Tsallis parameter used
                        example: 1.5
        '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

````