We discuss the prospects for a progress to be brought by ASTRO-H in the understanding of the physics of particle acceleration in astrophysical environments. Particular emphasis will be put on the synergy with gamma-ray astronomy, in the context of the rapid developments of recent years. Selected topics include: shock acceleration in supernova remnants (SNRs) and in clusters of galaxies, and the extreme particle acceleration seen in gamma-ray binaries. Since the hydrodynamics and thermal properties of shocks in these objects are covered in other white papers, we focus on the aspects related to the process of particle acceleration. In the case of SNRs, we emphasize the importance of SXS and HXI observations of the X-ray emission of young SNRs dominated by synchrotron radiation, particularly SNR RX J1713.7-3946. We argue that the HXI observations of young SNRs, as a byproduct of SXS observations dedicated for studies of the shock dynamics and nucleosynthesis, will provide powerful constraints on shock acceleration theories. Also, we discuss gamma-ray binary systems, where extreme particle acceleration is inferred regardless of the nature (a neutron star or a black hole) of the compact object. Finally, for galaxy clusters, we propose searches for hard X-ray emission of secondary electrons from interactions of ultra-high energy cosmic rays accelerated at accretion shocks. This should allow us to understand the contribution of galaxy clusters to the flux of cosmic rays above 10^18 eV.
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