General nonequilibrium theory of colloid dynamics
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A nonequilibrium extension of Onsager%27s canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile n (r,t) of a colloidal liquid in terms of the coupled time-evolution equations of its mean value n̄ (r,t) and of the covariance σ (r, r ′; t) δn (r,t) δn (r′, t) ̄ of its fluctuations δn (r,t) =n (r,t) - n̄ (r,t). These two coarse-grained equations involve a local mobility function b (r,t) which, in its turn, is written in terms of the memory function of the two-time correlation function C (r, r′; t, t′) δn (r,t) δn (r′, t′) ̄. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance n̄ 0 (r) and σ0 (r, r′) toward its equilibrium state characterized by the equilibrium local concentration profile n̄ eq (r) and equilibrium covariance σeq (r, r′). This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities. © 2010 The American Physical Society.
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A nonequilibrium extension of Onsager's canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile n (r,t) of a colloidal liquid in terms of the coupled time-evolution equations of its mean value n̄ (r,t) and of the covariance σ (r, r ′; t) δn (r,t) δn (r′, t) ̄ of its fluctuations δn (r,t) =n (r,t) - n̄ (r,t). These two coarse-grained equations involve a local mobility function b (r,t) which, in its turn, is written in terms of the memory function of the two-time correlation function C (r, r′; t, t′) δn (r,t) δn (r′, t′) ̄. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance n̄ 0 (r) and σ0 (r, r′) toward its equilibrium state characterized by the equilibrium local concentration profile n̄ eq (r) and equilibrium covariance σeq (r, r′). This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities. © 2010 The American Physical Society.
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Coarse-grained; Colloidal liquids; Colloidal particle; Concentration profiles; Effective interactions; Equilibrium state; External fields; Initial state; Irreversible process; Local mobility; Mean values; Memory functions; Non equilibrium; Nonequilibrium theory; Onsager; Spatial heterogeneity; Statistical properties; Theoretical framework; Thermal fluctuations; Time evolutions; Two-time correlation function; Statistical mechanics; Liquids
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