curl --request POST \
  --url https://api.fincept.in/quantlib/physics/boltzmann \
  --header 'Content-Type: application/json' \
  --header 'X-API-Key: <api-key>' \
  --data '
{
  "energies": [
    0,
    0.5,
    1.2,
    2.1,
    3.5
  ],
  "temperature": 1
}
'

{
  "success": true,
  "data": {
    "probabilities": [
      0.4066,
      0.2472,
      0.1504,
      0.0915,
      0.0336
    ],
    "partition_function": 2.4596,
    "average_energy": 1.2834,
    "energy_variance": 1.5623,
    "entropy": 1.3456,
    "free_energy": -0.7351,
    "heat_capacity": 0.6943
  }
}

{
  "detail": "Invalid API key"
}

{
  "detail": "Insufficient credits. This endpoint requires 5 credits."
}

{
  "detail": [
    {
      "loc": [
        "<string>"
      ],
      "msg": "<string>",
      "type": "<string>"
    }
  ]
}

quantlib-physics

Calculate Boltzmann Distribution Properties

Calculates properties of a Boltzmann distribution given energy levels and temperature. The Boltzmann distribution describes the probability of states in thermal equilibrium and can be applied to portfolio optimization, maximum entropy models, and market microstructure. Returns comprehensive thermodynamic properties including probabilities, partition function, average energy, entropy, free energy, and heat capacity.

Use Cases:

Maximum entropy portfolio optimization with return constraints
Model market equilibrium states
Calibrate energy-based models for risk
Analyze statistical mechanics of trading systems
Temperature-parameterized risk preferences

Formula: P(E_i) = exp(-E_i/T) / Z, where Z = Σ exp(-E_i/T)

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

POST

quantlib

physics

boltzmann

curl --request POST \
  --url https://api.fincept.in/quantlib/physics/boltzmann \
  --header 'Content-Type: application/json' \
  --header 'X-API-Key: <api-key>' \
  --data '
{
  "energies": [
    0,
    0.5,
    1.2,
    2.1,
    3.5
  ],
  "temperature": 1
}
'

{
  "success": true,
  "data": {
    "probabilities": [
      0.4066,
      0.2472,
      0.1504,
      0.0915,
      0.0336
    ],
    "partition_function": 2.4596,
    "average_energy": 1.2834,
    "energy_variance": 1.5623,
    "entropy": 1.3456,
    "free_energy": -0.7351,
    "heat_capacity": 0.6943
  }
}

{
  "detail": "Invalid API key"
}

{
  "detail": "Insufficient credits. This endpoint requires 5 credits."
}

{
  "detail": [
    {
      "loc": [
        "<string>"
      ],
      "msg": "<string>",
      "type": "<string>"
    }
  ]
}

Authorizations

X-API-Key

string

header

required

API key for authentication. Get your key at https://api.fincept.in/auth/register

Body

application/json

energies

number[]

required

Energy levels of states (can represent negative returns, costs, or losses)

Example:

[0, 1, 2, 3, 5]

temperature

number

required

Temperature parameter (higher = more uniform distribution, lower = concentrate on low energy)

Example:

1.5

Response

Boltzmann distribution calculated successfully

success

boolean

Example:

true

data

object

Show child attributes

Free Tier (0 credits)

Basic Tier (1 credit)

Standard Tier (2 credits)

Pro Tier (5 credits)

Enterprise Tier (10 credits)

Calculate Boltzmann Distribution Properties

Authorizations

Body

Response