Generalized Casimir forces in nonequilibrium systems

Abstract

In the present work, we propose a method to determine fluctuation-induced forces in nonequilibrium systems. These forces are the analog of the well-known Casimir forces, which were originally introduced in quantum field theory and later extended to the area of critical phenomena. The procedure starts from the observation that many nonequilibrium systems exhibit fluctuations with macroscopic correlation lengths, and the associated structure factors strongly depend on the wave vectors for long wavelengths; in some cases the correlations become long range, and the structure factors show algebraic divergences in the long-wavelength limit. The introduction of external bodies into such systems in general modifies the spectrum of these fluctuations, changing the value of the renormalized pressure, which becomes inhomogeneous. This inhomogeneous pressure leads to the appearance of a net force between the external bodies. It is shown that the force can be obtained from the knowledge of the structure factor of the homogeneous system. The mechanism is illustrated by means of a simple example: a reaction-diffusion equation, where the correlation function has a characteristic length. The role of this length in the Casimir force is elucidated.