Emergent dissipative quasi-particle picture in noninteracting Markovian open quantum systems Federico Carollo 1 and Vincenzo Alba 2 1 Institut f¨ ur Theoretische Physik, Universit¨ at T¨ ubingen, Auf der Morgenstelle 14, 72076 T¨ ubingen, Germany 2 Institute for Theoretical Physics, Universiteit van Amsterdam, Science Park 904, Postbus 94485, 1098 XH Amsterdam, The Netherlands Correlations between different regions of a quantum many-body system can be quantified through measures based on entropies of (reduced) subsystem states. For closed systems, several analytical and numerical tools, e.g., hydrodynamic theories or tensor networks, can accurately capture the time-evolution of subsystem entropies, thus allowing for a profound understanding of the unitary dynamics of quantum correlations. However, so far, these methods either cannot be applied to open quantum systems or do not permit an efficient computation of quantum entropies for mixed states. Here, we make progress in solving this issue by formulating a dissipative quasi-particle picture — describing the dynamics of quantum entropies in the hydrodynamic limit— for a general class of noninteracting open quantum systems. Our results show that also in dissipative many-body systems, correlations are generically established through the propagation of quasi-particles. Entropy plays a fundamental role in science [1]. In almost all its meanings, it provides a measure of disor- der for the state of a “physical” system. In thermody- namics, this provides the direction of the arrow of time while in information theory, it quantifies the uncertainty of the outcome of a random variable [2]. Remarkably, en- tropic functionals can capture correlations, e.g., through the mutual information [3–5], and for quantum systems they can characterize bipartite entanglement. This as- pect is receiving much attention nowadays, due to the growing interest in exploring universal behavior in the spreading of quantum correlations, either under unitary [6–24], dissipative [25–30] or stochastic dynamics [31–43]. In this work, we consider a subsystem embedded in a many-body quantum system, as sketched in Fig. 1(a). In particular, we are concerned with the time-evolution of R´ enyi and von Neumann entropies of the (reduced) sub- system state. For closed integrable quantum systems, at the hydrodynamic scale of large space-time coordinates, the dynamics of these entropies is captured by a quasi- particle picture [6, 8, 44–48]. In its simplest version, the initial state acts as a source of entangled pairs of quasi- particles, which spread with time through the whole sys- tem correlating different parts of it. To explain the ba- sic idea, lets consider the idealized situation of a many- body system containing a single pair, see Fig. 1(a). The two quasi-particles, labelled by their quasi-momentum q, propagate ballistically in opposite directions, with ve- locity ±|v q |. When they are shared by the subsystem and the remainder of the many-body system, [see star in Fig. 1(a)], these two parts get entangled, as witnessed by the subsystem state entropy assuming a finite value proportional to the entanglement of the pair [49]. While this picture (see Refs. [50–54] for extensions) has proved valuable for closed systems, it is not clear whether it can account for irreversible effects [cf. Fig. 1(b)]. As such, methods for analysing the open dynamics of quan- FIG. 1. Quasi-particle picture for closed systems and irreversible effects. a) We consider a subsystem of length ℓ embedded in a closed many-body system, whose initial state contains a single quasi-particle pair. Quasi-particles travel in opposite directions, with velocity ±|vq |. When one of the two enters the subsystem (see black star), the entropy of the sub- system state increases. b) For open systems, the many-body quantum state is mixed. This statistical uncertainty is re- sponsible for additional entropic contributions. Furthermore, quasi-particle densities are not conserved. tum correlations remain limited. In this paper, we make progress in this direction. Building on ideas put forward in a specific setting [29], we show that a dissipative quasi- particle picture describes the time-evolution of subsystem entropies, and of quantum correlations, for a general class of noninteracting open quantum systems. This picture is encoded in the formula S (n) ℓ (t)=  dq 2π  ℓs (n), mix q (t)+ + min(2|v q |t, ℓ)  s (n), YY q (t) − s (n), mix q (t)  , (1) providing the dynamics of the nth R´ enyi (also of the von Neumann) entropy S (n) ℓ , for a subsystem of length ℓ. Here, s (n), mix q ,s (n), YY q are two different entropic con- tributions. The first, s (n), mix q , is the contribution of the qth quasi-particles to the entropy of the full many-body mixed state, [cf. Fig. 1(b)]. On the other hand, s (n), YY q arXiv:2106.11997v1 [cond-mat.stat-mech] 22 Jun 2021