Definition:Entropic

Definition

Entropic Operation

Let $\circ$ be an operation on a set $S$ such that:

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

Then $\circ$ is entropic.

Entropic Structure

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

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 $13.12$