Related papers: Complexity of two-level systems
Entanglement is one of the physical properties of quantum systems responsible for the computational hardness of simulating quantum systems. But while the runtime of specific algorithms, notably tensor network algorithms, explicitly depends…
We propose and experimentally measure an entropy that quantifies the volume of correlations among qubits. The experiment is carried out on a nearly isolated quantum system composed of a central spin coupled and initially uncorrelated with…
The Renyi entropy is a generalization of the usual concept of entropy which depends on a parameter q. In fact, Renyi entropy is closely related to free energy. Suppose we start with a system in thermal equilibrium and then suddenly divide…
A measure of how sensitive the entanglement entropy is in a quantum system, has been proposed and its information geometric origin is discussed. It has been demonstrated for two exactly solvable spin systems, that thermodynamic criticality…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
We derive a family of entanglement criteria for continuous variable systems based on the R\'enyi entropy of complementary distributions. We show that these entanglement witnesses can be more sensitive than those based on second-order…
It is shown that the structure of thermodynamics is "form invariant", when it is derived using maximum entropy principle for various choices of entropy and even beyond equilibrium. By the form invariance of thermodynamics, it is meant that…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
The R\'enyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field $\lambda$ that controls the partition…
Many theoretical expressions of dissipation along non-equilibrium processes have been proposed. However, they have not been fully verified by experiments. Especially for systems strongly interacting with environments the connection between…
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…
The data-driven characterization of the ``complexity'' present in dynamical systems remains an open problem with broad applications across the physical sciences. We investigate the ``structural complexity'' of the 2D ferromagnetic Ising…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
We present a simple model which allows us to explain the physical nature of the oscillating entropy. We consider an ensemble of qubits interacting with thermal two-level systems. The entropy of the qubits oscillates between zero and the…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
The physical foundations of a variety of emerging technologies --- ranging from the applications of quantum entanglement in quantum information to the applications of nonequilibrium bulk and interface phenomena in microfluidics, biology,…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…