Asymmetric time-cross-correlation of nonequilibrium concentration fluctuations in a ternary liquid mixture

Equilibrium phenomena are characterized by time symmetry. Thermodynamic fluctuations are also time-symmetric at equilibrium. Conversely, diffusion of a solute in a liquid in the presence of a gradient is a nonequilibrium phenomenon, which gives rise to long-range fluctuations with amplitude much larger than the equilibrium one for small enough wave number. In the case of diffusion in binary mixtures such fluctuations are time-symmetric, notwithstanding the fact that they are generated by a nonequilibrium condition. In this paper, we investigate diffusion of two solutes in a ternary liquid mixture by means of fluctuating hydrodynamics theory. We show that the time-cross-correlation function of the concentrations is not time-symmetric, hence showing that time symmetry is violated for such nonequilibrium fluctuations. We discuss the feasibility of experiments aimed at the detection of the asymmetry of the cross-correlation function of nonequilibrium concentration fluctuations in ternary mixtures, as envisaged in the Giant Fluctuations (NEUF-DIX) microgravity project of the European Space Agency.

Figure 1

Residues of the integrand in Eq. (25) and integration paths.

Figure 2

Example of correlation function. The axes are arbitrary. The ratio between the two diffusion coefficients is 3.