Tsallis Entropy Calculator

Calculator

Input mode

Counts are converted to probabilities using pᵢ = nᵢ / Σnᵢ.

q (entropic index)

q ≈ 1 gives the Shannon limit.

k (scale factor)

Use k = 1 for dimensionless entropy.

Log base for Shannon limit

Used only when q is very close to 1.

Display precision

Controls rounding in the results table.

Auto-normalize probabilities

Trim zero entries

Auto-normalize affects probability mode only.

Values (one per line, or comma separated)

Provide pᵢ (probabilities) or nᵢ (counts) based on your selected mode.

A four-state distribution commonly used for demonstrations.

For this example, Σpᵢ^q = 0.5 and S_q = (1 − 0.5)/(1.5 − 1) = 1.0 when k = 1.

Tsallis entropy generalizes additive entropy for nonextensive systems:

S_q = k · (1 − Σ p_i^q) / (q − 1), q ≠ 1

Here, p_i are discrete probabilities, q controls sensitivity to rare or dominant states, and k is a scaling constant (often set to 1).

Shannon limit: as q approaches 1, the expression converges to:

S = −k · Σ p_i · log(p_i) / log(b)

b is the chosen log base (2 for bits, e for nats, 10 for digits).

Select Probabilities if you already have p_i values.
Select Counts if you have observations n_i; the tool converts them to probabilities.
Set q and k. Use q close to 1 to compare with the Shannon limit.
Paste values (one per line, or comma separated). Enable auto-normalize if needed.
Press Calculate. Results appear above the form, below the header.
Use Download CSV or Download PDF to export the report.