(…)

The collision entropy of a probability distribution on a finite set is the Rényi entropy at order 2:

$S_2(p)
\;=\;
-\log
\left(
\sum_{i=1}^n
p_i^2
\right)
\,,$

hence is the negative logarithm of the “collision probability”, i.e., of the probability that two independent random variables, both described by $p$, will take the same value.

order | $\phantom{\to} 0$ | $\to 1$ | $\phantom{\to}2$ | $\to \infty$ | ||||
---|---|---|---|---|---|---|---|---|

Rényi entropy | Hartley entropy | $\geq$ | Shannon entropy | $\geq$ | collision entropy | $\geq$ | min-entropy |

- G. M. Bosyk, M. Portesi, A. Plastino,
*Collision entropy and optimal uncertainty*, Phys. Rev. A 85 (2012) 012108 (arXiv:1112.5903)

See also:

- Wikipedia,
*Collision entropy*

Created on May 28, 2021 at 11:33:59. See the history of this page for a list of all contributions to it.