Mirror symmetry breaking with limited enantioselective autocatalysis and temperature gradients: a stability survey

We analyze limited enantioselective (LES) autocatalysis in a temperature gradient and with internal flow/recycling of hot and cold material. Microreversibility forbids broken mirror symmetry for LES in the presence of a temperature gradient alone. This symmetry can be broken however when the auto-catalysis and limited enantioselective catalysis are each localized within the regions of low and high temperature, respectively. This scheme has been recently proposed as a plausible model for spontaneous emergence of chirality in abyssal hydrothermal vents. Regions in chemical parameter space are mapped out in which the racemic state is unstable and bifurcates to chiral solutions

Fluctuation, Dissipation and the Arrow of Time

The recent development of the theory of fluctuation relations has led to new insights into the ever-lasting question of how irreversible behavior emerges from time-reversal symmetric microscopic dynamics. We provide an introduction to fluctuation relations, examine their relation to dissipation and discuss their impact on the arrow of time question.Comment: 12 pages, 3 figures. Minor Revisions. Accepted for publication in Entropy, Special Issue "Arrow of Time", edited by C. Callende

Quasichemical Models of Multicomponent Nonlinear Diffusion

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent diffusion based on the idea of the reaction mechanism borrowed from chemical kinetics. Chemical kinetics gave rise to very seminal tools for the modeling of processes. This is the stoichiometric algebra supplemented by the simple kinetic law. The results of this invention are now applied in many areas of science, from particle physics to sociology. In our work we extend the area of applications onto nonlinear multicomponent diffusion. We demonstrate, how the mechanism based approach to multicomponent diffusion can be included into the general thermodynamic framework, and prove the corresponding dissipation inequalities. To satisfy thermodynamic restrictions, the kinetic law of an elementary process cannot have an arbitrary form. For the general kinetic law (the generalized Mass Action Law), additional conditions are proved. The cell--jump formalism gives an intuitively clear representation of the elementary transport processes and, at the same time, produces kinetic finite elements, a tool for numerical simulation.Comment: 81 pages, Bibliography 118 references, a review paper (v4: the final published version

Spin-current noise from fluctuation relations

We present fluctuation relations that connect spin-polarized current and noise in mesoscopic conductors. In linear response, these relations are equivalent to the fluctuation-dissipation theorem that relates equilibrium current--current correlations to the linear conductance. More interestingly, in the weakly nonlinear regime of transport, these relations establish a connection between the leading-order rectification spin conductance, the spin noise susceptibility and the third cumulant of spin current fluctuations at equilibrium. Our results are valid even for systems in the presence of magnetic fields and coupled to ferromagnetic electrodes.Comment: Submitted to the Proceedings of the 31st ICP

Temperature in nonequilibrium systems with conserved energy

We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing to define a temperature T_{th} along the same lines as in the equilibrium microcanonical ensemble. The fluctuation-dissipation relation is explicitely found to be linear, but its slope differs from the inverse temperature T_{th}^{-1}. A numerical renormalization group procedure suggests that, at a coarse-grained level, all models behave similarly, leading to a two-parameter description of their macroscopic properties.Comment: 4 pages, 1 figure, final versio

Stochastic approach and fluctuation theorem for charge transport in diodes

A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction stochastic partial differential equations and the electric field generated by the charges is determined with the Poisson equation. These equations are discretized in space for the numerical simulations of the mean density profiles, the mean electric potential, and the current-voltage characteristics. Moreover, the full counting statistics of the carrier current and the measured total current including the contribution of the displacement current are investigated. On the basis of local detailed balance, the fluctuation theorem is shown to hold for both currents

Phase of Aharonov-Bohm oscillations in conductance of mesoscopic systems

Motivated by a recent experiment we analyze in detail the phase of Aharonov-Bohm oscillations across a 1D ring with a stub coupled to one of its arms, in the presence of a magnetic flux. We demonstrate that there are two kinds of conductance extremas. One class of them are fixed at particular flux values and can only change abruptly from a maxima to a minima as incident energy is varied. We show a different mechanism for such abrupt phase change in conductance oscillation. We demonstrate that these extremas can exhibit $``$phase locking". However, the second kind of extremas can shift continuously as the incident energy is varied.Comment: Figure available on reques