Temporal Asymmetry of Fluctuations in Nonequilibrium Steady States
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We conduct a comprehensive and systematic study of the temporal asymmetries of the fluctuations in properties of nonequilibrium, deterministic and reversible systems. Our motivation stems from the theories that predict asymmetry of fluctuation paths in stochastic dynamics. However, stochastic descriptions are an approximation in the sense that real systems obey deterministic reversible dynamics (at the classical level). In order to understand if the predicted asymmetry is an artifact of the stochastic model, we consider the results from studies of deterministic reversible systems composed of many particles. In order to examine these systems we used molecular dynamics simulations. We thoroughly investigate the presence of temporal asymmetry in the fluctuations of various properties in nonequilibrium, microscopic simulated systems, which are reversible and deterministic. We consider systems undergoing steady state Couette shear flow, and colour diffusion. For the first time we provide light on the particular path by which irreversibility emerges from microscopic reversible dynamics out of equilibrium. Asymmetry appears to be more accentuated in the larger the fluctuations. To assess the generality of temporal asymmetries in such deterministic systems, we consider identification of temporal asymmetries using differences of cross correlation functions: we establish from theoretical arguments and numerical evidence that a microscopic system undergoing colour diffusion exhibits asymmetry in a number of cross correlation functions. Furthermore we prove that some particular cross correlation functions have necessarily to be symmetric for a reversible and deterministic system to be regarded as “physical”. We then demonstrate how to mathematically express the fluctuation paths as a correlation function. We verify with strong numerical evidence that this equivalence holds for a simulated system. In light of this link between the asymmetry of correlation functions and that of fluctuation paths, we explain the presence of asymmetry in fluctuation paths via the transient time correlation formalism. We therefore give the first theoretical justification of the emergence of asymmetry in the fluctuations of microscopic deterministic and reversible systems. In this manner we are able to provide a sound theory to explain and characterize asymmetries in the fluctuations of mesoscopic systems. Finally we briefly outline possible future research directions.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Biomolecular and Physical Sciences
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