152
Appendix A
where = Mγ (units ≡ Kg/s)
In this system regardless of the potential’s symmetry, detailed balance is valid,
that is, the probability for a particle to make a thermally activated transition from
x to (x + x) equals the probability for the reverse step from (x + x) to x, for
arbitrary x and x. This implies that no exists net transport in thermal equilibrium.
To turn the system into a Brownian motor, one needs to break detailed balance
by driving the system away from thermal equilibrium, One way of doing so is to
introduce time dependent noise in the potential as 0.5 (1 + η DN (t)) V (x(t)) as the
case of flashing ratchet or adding a fluctuational force, η DN (t)F in the case of
rocking ratchet, where η DN (t) is dichotomous noise. That is why several authors
define a Brownian motor as a device that achieves directed motion of particles by
rectifying thermal fluctuations. We see that thermal fluctuations are crucial without
them does not exist movement of particles.
Appendix A
where = Mγ (units ≡ Kg/s)
In this system regardless of the potential’s symmetry, detailed balance is valid,
that is, the probability for a particle to make a thermally activated transition from
x to (x + x) equals the probability for the reverse step from (x + x) to x, for
arbitrary x and x. This implies that no exists net transport in thermal equilibrium.
To turn the system into a Brownian motor, one needs to break detailed balance
by driving the system away from thermal equilibrium, One way of doing so is to
introduce time dependent noise in the potential as 0.5 (1 + η DN (t)) V (x(t)) as the
case of flashing ratchet or adding a fluctuational force, η DN (t)F in the case of
rocking ratchet, where η DN (t) is dichotomous noise. That is why several authors
define a Brownian motor as a device that achieves directed motion of particles by
rectifying thermal fluctuations. We see that thermal fluctuations are crucial without
them does not exist movement of particles.