We employ time-dependent density matrix theory to characterize the concerted double-hydrogen transfer in benzoic acid dimers-the "system"-embedded in their crystalline environment-the "bath." The Liouville-von Neumann equation for the time evolution of the reduced nuclear density matrix is solved numerically, employing one- and two-dimensional models [R. Meyer and R. R. Ernst, J. Chem. Phys. 93, 5528 (1990)], the state representation for all operators and a matrix propagator based on Newton’s polynomials [M. Berman, R. Kosloff, and Il. Tal-Ezer, J. Phys. A 25, 1283 (1992)]. Dissipative processes such as environment-induced vibrational energy and phase relaxation, are accounted for within the Lindblad dynamical semigroup approach. The calculation of temperature-dependent relaxation matrix elements is based on a microscopic, perturbative theory proposed earlier [R. Meyer and R. R. Emst, J. Chem. Phys. 93, 5528 (1990)]. For the evaluation of the dissipative system dynamics, we compute (i) time-dependent state populations, (ii) energy and entropy flow between system and bath, (iii) expectation values for the hydrogen transfer coordinate, (iv) characteristic dephasing times and (v) temperature-dependent infrared spectra, determined with a recently proposed method by Neugebauer et al. Various "pure" and "thermal" nonequilibrium initial states are considered, and their equilibration with the bath followed in time.