A gas of Brownian particles in statistical dynamics |
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Authors: | R F Streater |
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Institution: | (1) Department of Mathematics, King's College, London, UK |
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Abstract: | We consider a large number of particles on a one-dimensional latticel
Z in interaction with a heat particle; the latter is located on the bond linking the position of the particle to the point
to which it jumps. The energy of a single particle is given by a potentialV(x), x∈Z. In the continuum limit, the classical version leads to Brownian motion with drift. A quantum version leads to a local drift
velocity which is independent of the applied force. Both these models obey Einstein's relation between drift, diffusion, and
applied force. The system obeys the first and second laws of thermodynamics, with the time evolution given by a pair of coupled
non linear heat equations, one for the density of the Brownian particles and one for the heat occupation number; the equation
for a tagged Brownian particle can be written as a stochastic differential equation. |
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Keywords: | Brownian motion nonlinear fluctuation-dissipation entropy stochastic differential equation |
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