Related papers: Effects of Noise on Entropy Evolution
We characterise the nonequilibrium stationary state of a generic multivariate Ornstein-Uhlenbeck process involving $N$ degrees of freedom. The irreversibility of the process is encoded in the antisymmetric part of the Onsager matrix. The…
Scalar conservation laws sit at the intersection between being simple enough to study analytically, while being complex enough to exhibit a wide range of nonlinear phenomena. We introduce a novel stochastic perturbation of scalar…
We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are quite different, the primary results remain the same. We find…
We discuss the concept of entropy applied to the infinite-N Kuramoto model and derive an expression for its time derivative. The time derivative of the entropy functional is shown to depend on the synchronization order parameter in a very…
We show non-linear stability and instability results in spherical symmetry for the interior of a charged black hole -approaching a sub-extremal Reissner-Nordstr\"om background fast enough at infinity- in presence of a massive and charged…
We theoretically study the decoherence of a two-level quantum system coupled to noisy environments exhibiting linear and quadratic fluctuations within the framework of a stochastic Liouville equation. It is shown that the intrinsic energy…
We study the von Neumann entropy asymptotics of pure translation-invariant quasi-free states of d-dimensional fermionic systems. It is shown that the entropic area law is violated by all these states: apart from the trivial cases, the…
For a class of idealized chaotic systems (hyperbolic systems) correlations decay exponentially in time. This result is asymptotic and rigorous. The decay rate is related to the Ruelle-Pollicott resonances. Nearly all chaotic model systems,…
Moving average processes driven by exponential-tailed L\'evy noise are important extensions of their Gaussian counterparts in order to capture deviations from Gaussianity, more flexible dependence structures, and sample paths with jumps.…
The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just…
In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…
We study the effect of local unitary noise on the entanglement evolution of a two-qubit system subject to local monitoring and inter-qubit coupling. We construct a stochastic Hamiltonian by incorporating the noise into the…
The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the…
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are…
Consciousness is supported by complex patterns of brain activity which are indicative of irreversible non-equilibrium dynamics. While the framework of stochastic thermodynamics has facilitated the understanding of physical systems of this…
Quantum coherence as an important physical resource plays the key role in implementing various quantum tasks, whereas quantum coherence is often deteriorated due to the noise. In this paper, we analyse under which dynamical conditions the…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…