We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector β, which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of the stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the β frame and Landau frame and present an instance where they differ.

We consider the non-equilibrium dynamics after a sudden quench of the magnetic field in the transverse field Ising chain starting from excited states of the pre-quench Hamiltonian. We prove that stationary values of local correlation functions can be described by the generalised Gibbs ensemble (GGE). Then we study the full time evolution of the transverse magnetisation by means of stationary phase methods. The equal time two-point longitudinal correlation function is analytically derived for a particular class of excited states for quenches within the ferromagnetic phase, and studied numerically in general. The full time dependence of the entanglement entropy of a block of spins is also obtained analytically for the same class of states and for arbitrary quenches.arXiv:1401.7250v1 [cond-mat.stat-mech]

We consider the asymptotic state after a sudden quench of the magnetic field in the transverse field quantum Ising chain starting from excited states of the pre-quench Hamiltonian. We compute the thermodynamic entropies of the generalised Gibbs and the diagonal ensembles and we find that the generalised Gibbs entropy is always twice the diagonal one. We show that particular care should be taken in extracting the thermodynamic limit since different averages of equivalent microstates give different results for the entropies.Entropy is a fundamental concept of statistical mechanics and represents the main bridge between the microscopic description of nature and thermodynamics. Indeed, a generic isolated classical system evolves in a way to maximise its entropy reaching the microcanonical ensemble after a long time. In the quantum world the situation is more complicated: an isolated system evolves unitarily, so if the system is initially prepared in a pure state it will always remain pure with strictly zero entropy, and cannot be described asymptotically by a statistical ensemble with positive entropy. The definition of a stationary entropy for non-equilibrium quantum systems is then a complicated matter which attracted renewed interest after the cold atom experimental realisation [1,2] of isolated out of equilibrium quantum systems, in particular of the so called quantum quenches [3,4], in which a parameter of the system is changed abruptly.Two main roads have been followed to define a nonequilibrium stationary entropy after a quench. The first is to look at the system in its entirety and define the entropy in a specific basis, such as for the so-called diagonal entropy [5]. The second road is to consider subsystems of the whole system which are not isolated and therefore are described by a reduced density matrix that may be equivalent to a statistical ensemble. The two roads have both their own advantages and disadvantages. Indeed, considering only a subsystem is probably more appropriate from a fundamental perspective because taking first the thermodynamic (TD) and then the large time limit (see e.g. [6-10]), it is possible that the reduced density matrix exhibits truly stationary behaviour which is impossible for the entire system. Conversely, a global definition of entropy is surely more suitable and manageable for finite systems and numerical simulations [11][12][13].The possible connections and relations between these two apparently unrelated sets of (stationary) entropies are then very important. Some explicit calculations for integrable systems in quenches from the ground state of a pre-quench Hamiltonian show that the diagonal entropy is exactly half of the subystem entropy [14,15], reflecting the fact that the diagonal ensemble contains much more information than the one needed to describe the local observables.However, the previous studies focused on the evolution starting from the ground state of a given pre-quench Hamiltonian. Starting from an excited state makes the situation more complicated. Indeed, ...

We study long-time dynamics of a bosonic system after suddenly switching on repulsive delta-like interactions. As initial states, we consider two experimentally relevant configurations: a rotating BEC and two counter-propagating BECs with opposite momentum, both on a ring. In the first case, the rapidity distribution function for the stationary state is derived analytically and it is given by the distribution obtained for the same quench starting from a BEC, shifted by the momentum of each boson. In the second case, the rapidity distribution function is obtained numerically for generic values of repulsive interaction and initial momentum. The significant differences for the case of large versus small quenches are discussed.