Directed and irreversible path in Euclidean spaces

The aim of this very short note is to relate the directed paths in $$ to the irreversible paths in $$. We first show that there is a directed path from $x$ to $y$ in ${\stackrel{\rm \longrightarrow}{\rm $\mathbb{R}$^n}}$ iff there exists an irreversible path with same initial and terminal points in $$. Also, we prove that every directed path in $$ is an irreversible path in $$.