Description
For mass strictly inside (0, 1), return log2((1 - mass)/mass).
Entropy summarizes uncertainty under a specified probability model and logarithm convention. Support indicators, one-symbol terms, and exponentiated entropies are components with different meanings.
For mass strictly inside (0, 1), return log2((1 - mass)/mass).
When to use this tool
Use Binary Entropy Local Slope when you need one explicitly scoped entropy or support calculation.
How to use the tool and how it works
- Enter mass. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read slope. Use the output convention below.
For mass strictly inside (0, 1), return log2((1 - mass)/mass).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| mass | Probability mass, dimensionless, in the stated domain. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| slope | Derivative with respect to the coordinate convention stated above. | Required. Finite number. |
{
"input": {
"mass": 0.5
},
"output": {
"slope": 0
}
}Limitations and assumptions
- This is the binary-entropy slope with respect to mass; endpoints with singular slope 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 Second Input Derivative
Return -1/[ln(2) × probability × (1 - probability)] for probability strictly inside (0, 1).
- Binary Entropy Logit Derivative
Return probability × (1 - probability) × log2((1 - probability)/probability), with endpoint values zero.