Description
Require probability in (0, 1] and multiply -(log2(probability) + 1/ln(2)) by delta for bitsChange.
Entropy summarizes uncertainty under a specified probability model and logarithm convention. Support indicators, one-symbol terms, and exponentiated entropies are components with different meanings.
Require probability in (0, 1] and multiply -(log2(probability) + 1/ln(2)) by delta for bitsChange.
When to use this tool
Use Entropy Probability Perturbation Linear Term when you need one explicitly scoped entropy or support calculation.
How to use the tool and how it works
- Enter probability, delta. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read bitsChange. Use the output convention below.
Require probability in (0, 1] and multiply -(log2(probability) + 1/ln(2)) by delta for bitsChange.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probability | Probability in the stated interval; zero handling follows the calculation above. | Required. Finite number; minimum 0; maximum 1; strictly above 0. |
| delta | Delta | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| bitsChange | Bits Change | Required. Finite number. |
{
"input": {
"probability": 0.5,
"delta": 0.1
},
"output": {
"bitsChange": -0.04426950408889634
}
}Limitations and assumptions
- This is a first-order change in one -p log2(p) term; delta need not preserve normalization and finite changes require higher-order analysis.
- 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 Local Slope
For mass strictly inside (0, 1), return log2((1 - mass)/mass).