Read the equation
The difference of consecutive V values divided by dt estimates its average rate over one discrete interval. It is not an exact continuous derivative unless an appropriate limiting or interpolation model is supplied. A negative observed difference is local evidence of decrease over that interval, not a proof for every future state.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| V | Candidate objective |
| dt | Nonzero elapsed step |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
inline double lyapunov_function(double omega, double coherence, double free_energy) {
double term1 = (omega - TARGET_OMEGA) * (omega - TARGET_OMEGA);
double term2 = LYAPUNOV_LAMBDA * (1.0 - coherence) * (1.0 - coherence);
double term3 = LYAPUNOV_MU * free_energy;
return term1 + term2 + term3;
}
// dV/dt = (V(t) - V(t-1))/dt
inline double lyapunov_derivative(double v_curr, double v_prev, double dt = 0.1) {
return (v_curr - v_prev) / dt;
}
// Gradient flow: dΩ/dt = -∇V(Ω)
inline double gradient_flow(double omega, double coherence, double free_energy) {
double grad_omega = 2.0 * (omega - TARGET_OMEGA);
double flow = -GRADIENT_ETA * grad_omega * omega * (1.0 - omega);
double coh_term = 0.001 * (1.0 - coherence);
double fe_term = 0.0005 * free_energy;Exact original notation
dV/dt = (V(t) - V(t-1))/dt