The Non-equilibrium Behavior of Fluctuation Induced Forces

Details The Non-equilibrium Behavior of Fluctuation Induced Forces The Non-equilibrium Behavior of Fluctuation Induced Forces

2009-03-05

arxiv.org/abs/0903.0933v1

J. Stat. Mech. (2009) L08001

Physics

Condensed Matter

Statistical Mechanics

4 pages RevTex, 2 .eps figures

Scientific paper

While techniques to compute thermal fluctuation induced, or pseudo-Casimir, forces in equilibrium systems are well established, the same is not true for non-equilibrium cases. We present a general formalism that allows us to unambiguously compute non-equilibrium fluctuation induced forces by specifying the energy of interaction of the fluctuating fields with the boundaries. For a general class of classical fields with dissipative dynamics, we derive a very general relation between the Laplace transform of the time-dependent force and the static partition function for a related problem with a different Hamiltonian. In particular, we demonstrate the power of our approach by computing, for the first time, the explicit time dependence of the non-equilibrium pseudo-Casimir force induced between two parallel plates, upon a sudden change in the temperature of the system. We also show how our results can be used to determine the steady-state behavior of the non-equilibrium force in systems where the fluctuations are driven by colored noise.

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