Presentation #115.11 in the session Multi-Messenger Astrophysics.
High-energy astrophysical systems, such as blazars, gamma-ray bursts, and pulsar wind nebulae, are powerful cosmic particle accelerators. There are increasing observational and theoretical evidence that the particle acceleration take places together with the magnetic field evolution. Probing the magnetic field evolution will shed light on the particle acceleration mechanisms. Polarimetry offers a direct measurement of the magnetic field. The recently launched IXPE has opened a new window on the X-ray polarization, and future missions such as COSI and AMEGO-X can explore the MeV polarization. Here I present theoretical predictions on the multi-wavelength polarization signatures for blazars, gamma-ray bursts, and pulsar wind nebulae. These predictions are derived from robust semi-analytical and numerical simulations, including spectral and temporal polarization signatures. These predictions, if detected by IXPE, COSI, and/or AMEGO-X, will provide unique constraints on the particle acceleration and multi-messenger signatures in these high-energy astrophysical systems.