In this paper, we study a Fokker-Planck equation of the form ut = I[u] + div(xu) where the operator I, which is usually the Laplacian, is replaced here with a general Lévy operator. We prove by the entropy production method the exponential decay in time of the solution to the only steady state of the associated stationnary equation.

We study the spatial asymptotics of Green’s function for 1d Schrödinger operator with operator-valued decaying potential. The bounds on entropy spectral measures are obtained. They used to establish presence a.c. spectrum.

We derive a modification of the semiclassical Fermi Golden Rule collision operator based on quantum thermodynamic principles. The resulting operator is nonlocal in space and acknowledges the presence of steep potential gradients and potential barriers. The resulting quantum mechanical transport equation the Wigner quantum Boltzmann equation increases the corresponding quantum mechanical entropy...

In this paper, we study a Fokker-Planck equation of the form ut = I[u] + div(xu) where the operator I, which is usually the Laplacian, is replaced here with a general Lévy operator. We prove by the entropy production method the exponential decay in time of the solution to the only steady state of the associated stationnary equation.

We revisit the construction of first-order spin hydrodynamics and find that constitution relations receive corrections from cross effects resulting spin-orbit coupling. Starting a routine entropy analysis, we show how to identify new transport coefficients second law thermodynamics. Interestingly, conventional coefficient heat conductivity $\kappa$ is bounded below by product coefficients, whic...

We nd a lower bound for the entropy dissipation of the spatially homogeneous Landau equation with hard potentials in terms of the entropy itself. We deduce from this explicit estimates on the speed of convergence towards equilibrium for the solution of this equation. In the case of so-called overmaxwellian potentials, the convergence is exponential. We also compute a lower bound for the spectra...

We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen phase-space decomposition. We prove that the Wigner separability entropy is equal to the operator space entanglement entropy, measuring entanglement in the spa...

Herein we study the problem of recovering a density operator from set compatible marginals, motivated limitations physical observations. Given that operators is not singular, adopt Jaynes' principle and wish to characterize with maximum entropy. We first show comparing entropy QSZK-complete, even for simplest case 3-chains. Then, focus on particular quantum Markov chains trees establish these c...

We define and investigate the notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme conditions and the entropy exchange computed with respect to any initial state supported on the code. In general the entropy of a code can be viewed as a ...