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The plasma of quarks and gluons created in ultrarelativistic heavy-ioncollisions turns out to be paramagnetic. In the presence of a backgroundmagnetic field, this paramagnetism thus leads to a pressure anisotropy, similarto anisotropies appearing in a viscous fluid. In the present paper, we use thisanalogy, and develop a framework similar to anisotropic hydrodynamics, to takethe pressure anisotropy caused, in particular, by the nonvanishingmagnetization of a plasma of quarks and gluons into account. We consider thefirst two moments of the classical Boltzmann equation in the presence of anelectromagnetic source in the relaxation-time approximation, and derive a setof coupled differential equations for the anisotropy parameter $\xi_0$ and theeffective temperature $\lambda_0$ of an ideal fluid with nonvanishingmagnetization. We also extend this method to a dissipative fluid with finitemagnetization in the presence of a strong and dynamical magnetic field. Wepresent a systematic method leading to the one-particle distribution functionof this magnetized dissipative medium in a first-order derivative expansion,and arrive at analytical expressions for the shear and bulk viscosities interms of the anisotropy parameter $\xi$ and effective temperature $\lambda$. Wethen solve the corresponding differential equations for $(\xi_0,\lambda_0)$ and$(\xi,\lambda)$ numerically, and determine, in this way, the proper time andtemperature dependence of the energy density, directional pressures, speed ofsound, and the magnetic susceptibility of a longitudinally expanding magnetizedquark-gluon plasma in and out of equilibrium.

Paramagnetic squeezing of a uniformly expanding quark-gluon plasma in and out of equilibrium