Read the equation
When the oscillatory contribution is assumed to average to zero and α is nonzero, α(E−C)=0 reduces to E=C. This is a consequence of that reduced balance. The original time-dependent system may instead have oscillations around its mean.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| E_star | Candidate averaged energy-like state |
| C_star | Candidate averaged C state |
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
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Original context
Read the surrounding source passage
\begin{equation}
\alpha(E^* - C^*) + \beta \cdot L^* \cdot \sin(\golden t) \cdot \golden = 0
\end{equation}
Time-averaging eliminates the oscillatory term (since $\langle \sin(\golden t) \rangle = 0$), yielding $E^* = C^*$.
Similarly, $dE/dt = 0$ at equilibrium gives:
\begin{equation}
-\gamma C^* + I^* \cdot (1 + \cos(\golden t \cdot \fib{n})) = 0
\end{equation}
The cosine term averages to zero for large Fibonacci numbers, giving $C^* = I^*/\gamma$.Exact original notation
E^* = C^*