Related papers: Average diagonal entropy in non-equilibrium isolat…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
The classical Hertz entropy is the logarithm of the volume of phase space bounded by the constant energy surface; its quantum counterpart, the quantum Hertz entropy, is $\hat S = k_B \ln \hat N$, where the quantum operator $\hat N$…
We calculate the average differential entropy of a $q$-component Gaussian mixture in $\mathbb R^n$. For simplicity, all components have covariance matrix $\sigma^2 {\mathbf 1}$, while the means $\{\mathbf{W}_i\}_{i=1}^{q}$ are i.i.d.…
We study the internal dynamics of an elementary quantum system placed close to a body held at a temperature different from that of the surrounding radiation. We derive general expressions for lifetime and density matrix valid for bodies of…
Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary…
Entropy production is a key quantity characterizing nonequilibrium systems. However, it can often be difficult to compute in practice, as it requires detailed information about the system and the dynamics it undergoes. This becomes even…
In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied…
We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non- Hermitian case and find…
We study quantum coarse-grained entropy and demonstrate that the gap in entropy between local and global coarse-grainings is a natural generalization of entanglement entropy to mixed states and multipartite systems. This "quantum…
The large-scale properties of homogeneous states after quantum quenches in integrable systems have been successfully described by a semiclassical picture of moving quasiparticles. Here we consider the generalisation for the entanglement…
We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are…
The development and spread of entanglement in complex quantum systems is central to exploring many-body phenomena out of equilibrium. Measuring entanglement dynamics can shed light on information scrambling and thermalisation, namely on…
The thermodynamic implications for the out-of-equilibrium dynamics of quantum systems are to date largely unexplored, especially for quantum many-body systems. In this paper we investigate the paradigmatic case of an array of…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
We study the unitary time evolution of the order parameter of a quantum system after a sudden quench in the parameter driving the transition. By mapping the dynamics onto the imaginary time path-integral in a film geometry we derive the…
For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and…
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been…
Entropy production is one of the most important characteristics of non-equilibrium steady states. We study here the steady-state entropy production, both at short times as well as in the long-time limit, of two important classes of…
The classical Second Law of Thermodynamics demands that an isolated system evolves with a non-diminishing entropy. This holds as well in quantum mechanics if the evolution of the energy-isolated system can be described by a unital quantum…
The nonequilibrium dynamics of coupled quantum oscillators subject to different time dependent quenches are analyzed in the context of the Liouville-von Neumann approach. We consider models of quantum oscillators in interaction that are…