6 research outputs found
The law of action and reaction for the effective force in a nonequilibrium colloidal system
We study a nonequilibrium Langevin many-body system containing two 'test'
particles and many 'background' particles. The test particles are spatially
confined by a harmonic potential, and the background particles are driven by an
external driving force. Employing numerical simulations of the model, we
formulate an effective description of the two test particles in a
nonequilibrium steady state. In particular, we investigate several different
definitions of the effective force acting between the test particles. We find
that the law of action and reaction does not hold for the total mechanical
force exerted by the background particles, but that it does hold for the
thermodynamic force defined operationally on the basis of an idea used to
extend the first law of thermodynamics to nonequilibrium steady states.Comment: 13 page
Exact transformation of a Langevin equation to a fluctuating response equation
We demonstrate that a Langevin equation that describes the motion of a
Brownian particle under non-equilibrium conditions can be exactly transformed
to a special equation that explicitly exhibits the response of the velocity to
a time dependent perturbation. This transformation is constructed on the basis
of an operator formulation originally used in nonlinear perturbation theory for
differential equations by extending it to stochastic analysis. We find that the
obtained expression is useful for the calculation of fundamental quantities of
the system, and that it provides a physical basis for the decomposition of the
forces in the Langevin description into effective driving, dissipative, and
random forces in a large-scale description.Comment: 14 pages, to appear in J. Phys. A: Math. Ge