Complex algebras of subalgebras

Let $\mathcal V$ be a variety of algebras. We specify a condition (the so-called generalized entropic property), which is equivalent to the fact that for every algebra $\mathbf A\in\mathcal V$, the set of all subalgebras of $\mathbf A$ is a subuniverse of the complex algebra of the subalgebras of $\mathbf A$. The relationship between the generalized entropic property and the entropic law is investigated. Also, for varieties with the generalized entropic property, we consider identities that are satisfied by complex algebras of subalgebras.