Definition:Entropic Structure

Definition

An entropic structure is an algebraic structure $\struct {S, \circ}$ such that $\circ$ is an entropic operation.

That is, such that:

$\forall a, b, c, d \in S: \paren {a \circ b} \circ \paren {c \circ d} = \paren {a \circ c} \circ \paren {b \circ d}$

Also known as

An entropic structure is also known as a medial structure.

Also see

• Results about entropic structures can be found here.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 13$: Compositions Induced on Cartesian Products and Function Spaces: Exercise $13.12$