  The entropy of a tropical ideal is introduced. The radical of a tropical
ideal consists of all tropical polynomials vanishing on the tropical prevariety
determined by the ideal. We prove that the entropy of the radical of a tropical
bivariate polynomial with vanishing coefficients equals zero. Also we prove
that the entropy of a zero-dimensional tropical prevariety vanishes. An example
of a non-radical tropical ideal having a positive entropy is exhibited.
