Abstract
Abstract
We consider a classical Brownian oscillator of mass m driven from an arbitrary initial state by varying the stiffness k(t) of the harmonic potential according to the protocol
k
(
t
)
=
k
0
+
a
δ
(
t
)
, involving the Dirac delta function. The microscopic work performed on the oscillator is shown to be
W
=
(
a
2
/
2
m
)
q
2
−
a
q
v
, where q and v are the coordinate and velocity in the initial state. If the initial distribution of q and v is the equilibrium one with temperature T, the average work is
⟨
W
⟩
=
a
2
T
/
(
2
m
k
0
)
and the distribution f(W) has the form of the product of exponential and modified Bessel functions. The distribution is asymmetric and diverges as W → 0. The system’s response for t > 0 is evaluated for specific models.