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

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

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

Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics

An overview is given of recent advances in nonequilibrium statistical mechanics on the basis of the theory of Hamiltonian dynamical systems and in the perspective provided by the nanosciences. It is shown how the properties of relaxation toward a state of equilibrium can be derived from Liouville's equation for Hamiltonian dynamical systems. The relaxation rates can be conceived in terms of the so-called Pollicott-Ruelle resonances. In spatially extended systems, the transport coefficients can also be obtained from the Pollicott-Ruelle resonances. The Liouvillian eigenstates associated with these resonances are in general singular and present fractal properties. The singular character of the nonequilibrium states is shown to be at the origin of the positive entropy production of nonequilibrium thermodynamics. Furthermore, large-deviation dynamical relationships are obtained which relate the transport properties to the characteristic quantities of the microscopic dynamics such as the Lyapunov exponents, the Kolmogorov-Sinai entropy per unit time, and the fractal dimensions. We show that these large-deviation dynamical relationships belong to the same family of formulas as the fluctuation theorem, as well as a new formula relating the entropy production to the difference between an entropy per unit time of Kolmogorov-Sinai type and a time-reversed entropy per unit time. The connections to the nonequilibrium work theorem and the transient fluctuation theorem are also discussed. Applications to nanosystems are described.Comment: Lecture notes for the International Summer School Fundamental Problems in Statistical Physics XI (Leuven, Belgium, September 4-17, 2005

Fluctuation relations for equilibrium states with broken discrete symmetries

Relationships are obtained expressing the breaking of spin-reversal symmetry by an external magnetic field in Gibbsian canonical equilibrium states of spin systems under specific assumptions. These relationships include an exact fluctuation relation for the probability distribution of the magnetization, as well as a relation between the standard thermodynamic entropy, an associated spin-reversed entropy or coentropy, and the product of the average magnetization with the external field, as a non-negative Kullback-Leibler divergence. These symmetry relations are applied to the model of noninteracting spins, the 1D and 2D Ising models, and the Curie-Weiss model, all in an external magnetic field. The results are drawn by analogy with similar relations obtained in the context of nonequilibrium physics

Signatures of classical bifurcations in the quantum scattering resonances of dissociating molecules

A study is reported of the quantum scattering resonances of dissociating molecules using a semiclassical approach based on periodic-orbit theory. The dynamics takes place on a potential energy surface with an energy barrier separating two channels of dissociation. Above the barrier, the unstable symmetric-stretch periodic orbit may undergo a supercritical pitchfork bifurcation, leading to a classically chaotic regime. Signatures of the bifurcation appear in the spectrum of resonances, which have a shorter lifetime than classically expected. A method is proposed to evaluate semiclassically the energy and lifetime of the quantum resonances in this intermediate regime

Kinetics and thermodynamics of DNA polymerases with exonuclease proofreading

Kinetic theory and thermodynamics are applied to DNA polymerases with exonuclease activity, taking into account the dependence of the rates on the previously incorportated nucleotide. The replication fidelity is shown to increase significantly thanks to this dependence at the basis of the mechanism of exonuclease proofreading. In particular, this dependence can provide up to a hundred-fold lowering of the error probability under physiological conditions. Theory is compared with numerical simulations for the DNA polymerases of T7 viruses and human mitochondria.Comment: Physical Review E (2016

Nonlinear transport effects in mass separation by effusion

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