  We address the out-of-equilibrium dynamics arising from quantum-quench (QQ)
protocols (instantaneous changes of the Hamiltonian parameters) in many-body
systems within their quantum critical regime and in contact with thermal baths,
homogeneously coupled to the systems. We consider two classes of QQ protocols.
One of them uses the thermal bath to prepare the initial Gibbs state; then,
after quenching, the thermal bath is removed and the dynamics of the system is
unitary. Wealso address a more complex QQ protocol where the thermal bath is
not removed after quenching, thus the quantum evolution is also driven by the
interaction with the bath, which may be described by appropriate master
equations for the density matrix of the system, where a further relevant time
scale, or inverse decay rate, characterizes the system-bath coupling. Under
these QQ protocols, the critical system develops out-of-equilibrium scaling
behaviors, which extend those forisolated critical systems, by introducing
further scaling variables proportional to the temperature and the decay rate
associated with the thermal baths. These out-of-equilibrium scaling behaviors
are checked by analyzing QQ protocols within fermionic Kitaev wires, or
equivalently quantum Ising chains, supplemented with a particular modelization
of thermal bath that guarantees the asymptotic thermalization within the
Lindblad master equation for the dynamics of open systems.
