Nonlinear response theory for inhomogeneous systems in various ensembles

Nonlinear equations governing the relaxation of some macroscopic quantities, a(r,t) are derived using Kubo's response theory, in isolated inhomogeneous systems. The resulting equations contain microcanonical time correlation functions. It is shown how to express these in terms of arbitrary ensemble correlation functions and correction arising from their infinite time behaviour are discussed. In addition it is shown that the concept of local equilibrium must be modified somewhat.     

Mode coupling theory of hydrodynamics and steady state systems

We construct a formal mode coupling theory for hydrodynamic systems which includes contributions from all powers of the hydrodynamic variables. This theory is applied to nonequilibrium steady state systems. A generalization of the local equilibrium distribution is used to describe the nonequilibrium state. This distribution independently constrains all moments of the hydrodynamic variables. The infinite hierarchy of equations for the moments of the hydrodynamic variables is truncated using an inverse system size expansion. Explicit results are obtained for the time correlation functions of fluids with a linear temperature gradient or a linear shear. These results agree with previous studies of these steady states.     

Transport in two dimensions. II the thermal conductivity coefficient

The study of generalized transport coefficients in two dimensions is continued. In this article, the thermal conductivity coefficient is examined. The Mori formalism is used and the set of variables consists of all finite multilinear products of two collective conserved variables, the energy density and the momentum density. The tensorial symmetry of Euler and dissipative matrix elements is taken into account explicitly. Two simultaneous non-linear integral equations are obtained, the asymptotic solution for which behave in the same manner as the self-diffusion coefficient studied in an earlier paper. However, the coefficient is dependent upon the intermolecular potential. The heat current auto-correlation function decays asymptotically as $\text{[t}\text{In}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{t]}{}^{\mathrm{?1}}$. The asymptotic form for the shear viscosity coefficient is examined briefly and found to be independent of the intermolecular potential. A better approximation for the coefficient of the asymptotic form of the self-diffusion coefficient is presented.     

Transport in two dimensions. III self-diffusion coefficient at low densities

The low density form of the generalized frequency (s) and wavevector (k) dependent self-diffusion coefficient D(k, s) is calculated, from which the low density forms of related quantities, e.g. the velocity autocorrelation function, are derived. Agreement is obtained with the low density kinetic theory results. A closed form expression for D(k, s) valid over a wide range of densities and times is also given, showing consistency between the asymptotic long time results, obtained previously, and the low density kinetic theory results.     

An exact treatment of some integrals appearing in the three-body contributions to transport coefficients

The convergence properties of the integral corresponding to the three-body cyclic collisions in the two-dimensional density expansion of transport coefficients are investigated. It is shown exactly that the integral considered by Oppenheim et al. and by Eu diverges logarithmically in the switching parameter ε.     

Distillation protocols: output entanglement and local mutual information

A complementary behavior between local mutual information and average output entanglement is derived for arbitrary bipartite ensembles. This leads to bounds on the yield of entanglement in distillation protocols that involve disinguishing. This bound is saturated in the hashing protocol for distillation, for Bell-diagonal states.     

Thermodynamical approach to quantifying quantum correlations

We consider the amount of work which can be extracted from a heat bath using a bipartite state rho shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this "work deficit" and calculate it explicitly for a number of different cases. In particuar, for pure states the work deficit is exactly equal to the distillable entanglement of the state. A form of complementarity exists between physical work which can be extracted and distillable entanglement. The work deficit is a good measure of the quantum correlations in a state and provides a new paradigm for understanding quantum nonlocality.