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Statistical Mechanics operators

20 operators in the statistical_mechanics category of the live registry. Compose them in a contract or call POST /api/zeq/compute — KO42 is always on, plus up to three more per call.

How it computes: dedicated closed-form solver solveSM — real equations over CODATA-2018 constants; where an operator needs a series/matrix/field a scalar cannot express, it refuses honestly. See the solvers.

OperatorDescriptionEquation
EQP1Equipartition theorem: each quadratic degree of freedom carries a mean energy of ½k_BT, so a system with f quadratic DOF has ⟨E⟩ = (f/2)k_BT.⟨E⟩ = (f/2) k_B T
MBS1Maxwell–Boltzmann speed distribution characteristic speeds: most-probable √(2kT/m), mean √(8kT/πm) and root-mean-square √(3kT/m) for an ideal gas at temperature T.v_rms = √(3k_BT/m)
NE1Point kinetics neutron equation: rate of change of neutron population with delayed neutron precursors.\frac{dn}{dt} = (k-1)\frac{n}{\ell} + \sum_i \lambda_i C_i
NE10Four-factor formula: infinite multiplication factor from reproduction, fast fission, resonance escape, and thermal utilization.k_\infty = \eta f p \epsilon
NE11Effective multiplication with non-leakage probability for finite reactor geometry.k_{eff} = k_\infty P_{NL}
NE12Buckling equation: geometric condition for criticality balancing neutron production and leakage.B^2 = \frac{k_\infty - 1}{L^2 + \tau}
NE13Diffusion length: characteristic distance a thermal neutron diffuses before absorption.L = \sqrt{\frac{D}{\Sigma_a}}
NE14Reactor power from neutron flux, fission cross-section, energy per fission, and volume.P = \Phi\Sigma_f E_f V
NE15Heat generation rate distribution in a cylindrical reactor core.q''' = q_0 \cos\frac{\pi z}{H}J_0(2.405 r/R)
NE16Thermal efficiency of a heat engine as one minus cold-to-hot temperature ratio.\eta_{th} = 1 - \frac{T_C}{T_H}
NE17Coolant mass flow rate required to remove reactor heat at given temperature rise.\dot{m} = \frac{Q}{c_p \Delta T}
NE2Delayed neutron precursor equation: production from fission minus decay for reactor kinetics.\frac{dC_i}{dt} = \beta_i\frac{n}{\ell} - \lambda_i C_i
NE3Effective multiplication factor: ratio of neutrons produced to neutrons lost in a reactor.k_{eff} = \frac{\text{neutrons produced}}{\text{neutrons lost}}
NE4Reactivity: fractional departure of multiplication factor from unity.\rho = \frac{k-1}{k}
NE5Reactor period: e-folding time for neutron population change.T = \frac{\ell}{(k-1)(1-\beta)}
NE6Macroscopic cross-section: number density times microscopic cross-section for neutron interactions.\Sigma = N\sigma
NE7Neutron flux: product of neutron density and speed, measuring interaction rate intensity.\Phi = nv
NE8Reaction rate: macroscopic cross-section times neutron flux for nuclear reaction rates.R = \Sigma\Phi
NE9Reproduction factor eta: average neutrons produced per absorption in fuel.\eta = \frac{\nu\Sigma_f}{\Sigma_a}
XI0Bosonic partition function: product over states of the geometric series factor.φ × ∑min(I(p), I(¬p))

Compute one — a real call​

Ask the operator which inputs it needs (the honesty contract refuses empty inputs rather than inventing them):

curl -sS -X POST https://zeqsdk.com/api/zeq/operator-spec \
  -H "Content-Type: application/json" \
  -d '{"operator":"EQP1"}'

See also​