Statistical Mechanics operators

18 operators in the statistical_mechanics category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

Operator	Description	Equation
`NE1`	Point 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`
`NE10`	Four-factor formula: infinite multiplication factor from reproduction, fast fission, resonance escape, and thermal utilization.	`k_\infty = \eta f p \epsilon`
`NE11`	Effective multiplication with non-leakage probability for finite reactor geometry.	`k_{eff} = k_\infty P_{NL}`
`NE12`	Buckling equation: geometric condition for criticality balancing neutron production and leakage.	`B^2 = \frac{k_\infty - 1}{L^2 + \tau}`
`NE13`	Diffusion length: characteristic distance a thermal neutron diffuses before absorption.	`L = \sqrt{\frac{D}{\Sigma_a}}`
`NE14`	Reactor power from neutron flux, fission cross-section, energy per fission, and volume.	`P = \Phi\Sigma_f E_f V`
`NE15`	Heat generation rate distribution in a cylindrical reactor core.	`q''' = q_0 \cos\frac{\pi z}{H}J_0(2.405 r/R)`
`NE16`	Thermal efficiency of a heat engine as one minus cold-to-hot temperature ratio.	`\eta_{th} = 1 - \frac{T_C}{T_H}`
`NE17`	Coolant mass flow rate required to remove reactor heat at given temperature rise.	`\dot{m} = \frac{Q}{c_p \Delta T}`
`NE2`	Delayed neutron precursor equation: production from fission minus decay for reactor kinetics.	`\frac{dC_i}{dt} = \beta_i\frac{n}{\ell} - \lambda_i C_i`
`NE3`	Effective multiplication factor: ratio of neutrons produced to neutrons lost in a reactor.	`k_{eff} = \frac{\text{neutrons produced}}{\text{neutrons lost}}`
`NE4`	Reactivity: fractional departure of multiplication factor from unity.	`\rho = \frac{k-1}{k}`
`NE5`	Reactor period: e-folding time for neutron population change.	`T = \frac{\ell}{(k-1)(1-\beta)}`
`NE6`	Macroscopic cross-section: number density times microscopic cross-section for neutron interactions.	`\Sigma = N\sigma`
`NE7`	Neutron flux: product of neutron density and speed, measuring interaction rate intensity.	`\Phi = nv`
`NE8`	Reaction rate: macroscopic cross-section times neutron flux for nuclear reaction rates.	`R = \Sigma\Phi`
`NE9`	Reproduction factor eta: average neutrons produced per absorption in fuel.	`\eta = \frac{\nu\Sigma_f}{\Sigma_a}`
`XI0`	Bosonic partition function: product over states of the geometric series factor.	`φ × ∑min(I(p), I(¬p))`

Compute with one of these

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["NE1"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

Compute with one of these​

See also​

Compute with one of these

See also