  We study the azimuthal angle dependence of the energy-energy correlators
$\langle \mathcal{E}(\hat{n}_1)\mathcal{E}(\hat{n}_2)\rangle$ in the
back-to-back region for $e^+e^-$ annihilation and deep inelastic scattering
(DIS) processes with general polarization of the proton beam. We demonstrate
that the polarization information of the beam and the underlying partons from
the hard scattering is propagated into the azimuthal angle dependence of the
energy-energy correlators. In the process, we define the Collins-type EEC jet
functions and introduce a new EEC observable using the lab-frame angles in the
DIS process. Furthermore, we extend our formalism to explore the two-point
energy correlation between hadrons with different quantum numbers
$\mathbb{S}_i$ in the back-to-back limit $\langle
\mathcal{E}_{\mathbb{S}_1}(\hat{n}_1)\mathcal{E}_{\mathbb{S}_2}(\hat{n}_2)\rangle$.
We find that in the Operator Product Expansion (OPE) region the nonperturbative
information is entirely encapsulated by a single number. Using our formalism,
we present several phenomenological studies that showcase how energy
correlators can be used to probe transverse momentum dependent structures.
