Description
Return -1/[ln(2) × probability × (1 - probability)] for probability strictly inside (0, 1).
Entropy summarizes uncertainty under a specified probability model and logarithm convention. Support indicators, one-symbol terms, and exponentiated entropies are components with different meanings.
Return -1/[ln(2) × probability × (1 - probability)] for probability strictly inside (0, 1).
When to use this tool
Use Binary Entropy Second Input Derivative when you need one explicitly scoped entropy or support calculation.
How to use the tool and how it works
- Enter probability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Return -1/[ln(2) × probability × (1 - probability)] for probability strictly inside (0, 1).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probability | Probability in the stated interval; zero handling follows the calculation above. | Required. Finite number; strictly above 0; strictly below 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"probability": 0.5
},
"output": {
"derivative": -5.7707801635558535
}
}Limitations and assumptions
- This is the second derivative of binary entropy in bits with respect to probability; singular endpoints are rejected.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Validate and align complete probability distributions before aggregating terms or interpreting an uncertainty estimate.
References
Similar or alternative tools
- Binary Entropy Local Slope
For mass strictly inside (0, 1), return log2((1 - mass)/mass).
- Binary Entropy Curvature Term
Return -1/[probability × (1 - probability) × ln(logBase)].