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

portfolio_states

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 } '

200

{
  "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
  }
}

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

200

application/json

Boltzmann distribution calculated successfully

success · boolean

Example:

true

data · object

Show child attributes