646 research outputs found

    Self-Organization at the Nanoscale Scale in Far-From-Equilibrium Surface Reactions and Copolymerizations

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    An overview is given of theoretical progress on self-organization at the nanoscale in reactive systems of heterogeneous catalysis observed by field emission microscopy techniques and at the molecular scale in copolymerization processes. The results are presented in the perspective of recent advances in nonequilibrium thermodynamics and statistical mechanics, allowing us to understand how nanosystems driven away from equilibrium can manifest directionality and dynamical order.Comment: A. S. Mikhailov and G. Ertl, Editors, Proceedings of the International Conference "Engineering of Chemical Complexity", Berlin Center for Studies of Complex Chemical Systems, 4-8 July 201

    Growth and dissolution of macromolecular Markov chains

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    The kinetics and thermodynamics of free living copolymerization are studied for processes with rates depending on k monomeric units of the macromolecular chain behind the unit that is attached or detached. In this case, the sequence of monomeric units in the growing copolymer is a kth-order Markov chain. In the regime of steady growth, the statistical properties of the sequence are determined analytically in terms of the attachment and detachment rates. In this way, the mean growth velocity as well as the thermodynamic entropy production and the sequence disorder can be calculated systematically. These different properties are also investigated in the regime of depolymerization where the macromolecular chain is dissolved by the surrounding solution. In this regime, the entropy production is shown to satisfy Landauer's principle

    Nonlinear transport effects in mass separation by effusion

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    Generalizations of Onsager reciprocity relations are established for the nonlinear response coefficients of ballistic transport in the effusion of gaseous mixtures. These generalizations, which have been established on the basis of the fluctuation theorem for the currents, are here considered for mass separation by effusion. In this kinetic process, the mean values of the currents depend nonlinearly on the affinities or thermodynamic forces controlling the nonequilibrium constraints. These nonlinear transport effects are shown to play an important role in the process of mass separation. In particular, the entropy efficiency turns out to be significantly larger than it would be the case if the currents were supposed to depend linearly on the affinities

    Fluctuation relations for equilibrium states with broken discrete or continuous symmetries

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    Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues obtained for non-equilibrium systems where the broken symmetry is time reversal. At equilibrium, these relations show that the ratio of the probabilities of opposite fluctuations goes exponentially with the symmetry-breaking external field and the magnitude of the fluctuations. These relations are applied to the Curie-Weiss, Heisenberg, and XYXY~models of magnetism where the continuous rotational symmetry is broken, as well as to the qq-state Potts model and the pp-state clock model where discrete symmetries are broken. Broken symmetries are also considered in the anisotropic Curie-Weiss model. For infinite systems, the results are calculated using large-deviation theory. The relations are also applied to mean-field models of nematic liquid crystals where the order parameter is tensorial. Moreover, their extension to quantum systems is also deduced.Comment: 34 pages, 14 figure

    Quantum master equation for the microcanonical ensemble

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    By using projection superoperators, we present a new derivation of the quantum master equation first obtained by the Authors in Phys. Rev. E {\bf 68}, 066112 (2003). We show that this equation describes the dynamics of a subsystem weakly interacting with an environment of finite heat capacity and initially described by a microcanonical distribution. After applying the rotating wave approximation to the equation, we show that the subsystem dynamics preserves the energy of the total system (subsystem plus environment) and tends towards an equilibrium state which corresponds to equipartition inside the energy shell of the total system. For infinite heat capacity environments, this equation reduces to the Redfield master equation for a subsystem interacting with a thermostat. These results should be of particular interest to describe relaxation and decoherence in nanosystems where the environment can have a finite number of degrees of freedom and the equivalence between the microcanonical and the canonical ensembles is thus not always guaranteed.Comment: 8 pages, 0 figures; v2: typos in eq 42 and 43 corrected; v3: submitted to Phys.Rev.E; v4: accepted in Phys.Rev.
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