<s>
The	O
Onsager	B-Algorithm
–	I-Algorithm
Machlup	I-Algorithm
function	I-Algorithm
is	O
a	O
function	O
that	O
summarizes	O
the	O
dynamics	O
of	O
a	O
continuous	O
stochastic	O
process	O
.	O
</s>
<s>
as	O
,	O
where	O
is	O
the	O
Onsager	B-Algorithm
–	I-Algorithm
Machlup	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
Consider	O
a	O
-dimensional	O
Riemannian	B-Architecture
manifold	I-Architecture
and	O
a	O
diffusion	O
process	O
on	O
with	O
infinitesimal	O
generator	O
,	O
where	O
is	O
the	O
Laplace	O
–	O
Beltrami	O
operator	O
and	O
is	O
a	O
vector	O
field	O
.	O
</s>
<s>
where	O
is	O
the	O
Riemannian	O
distance	O
,	O
denote	O
the	O
first	B-Algorithm
derivatives	I-Algorithm
of	O
,	O
and	O
is	O
called	O
the	O
Onsager	B-Algorithm
–	I-Algorithm
Machlup	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
where	O
is	O
the	O
Riemannian	O
norm	O
in	O
the	O
tangent	O
space	O
at	O
,	O
is	O
the	O
divergence	B-Application
of	O
at	O
,	O
and	O
is	O
the	O
scalar	O
curvature	O
at	O
.	O
</s>
<s>
The	O
following	O
examples	O
give	O
explicit	O
expressions	O
for	O
the	O
Onsager	B-Algorithm
–	I-Algorithm
Machlup	I-Algorithm
function	I-Algorithm
of	O
a	O
continuous	O
stochastic	O
processes	O
.	O
</s>
<s>
The	O
Onsager	B-Algorithm
–	I-Algorithm
Machlup	I-Algorithm
function	I-Algorithm
can	O
be	O
used	O
for	O
purposes	O
of	O
reweighting	O
and	O
sampling	O
trajectories	O
,	O
</s>
