<s>
In	O
computer	B-Application
simulations	I-Application
of	O
mechanical	O
systems	O
,	O
energy	B-Algorithm
drift	I-Algorithm
is	O
the	O
gradual	O
change	O
in	O
the	O
total	O
energy	O
of	O
a	O
closed	O
system	O
over	O
time	O
.	O
</s>
<s>
However	O
,	O
in	O
simulations	O
the	O
energy	O
might	O
fluctuate	O
on	O
a	O
short	O
time	O
scale	O
and	O
increase	O
or	O
decrease	O
on	O
a	O
very	O
long	O
time	O
scale	O
due	O
to	O
numerical	B-Algorithm
integration	I-Algorithm
artifacts	O
that	O
arise	O
with	O
the	O
use	O
of	O
a	O
finite	O
time	O
step	O
Δt	O
.	O
</s>
<s>
This	O
is	O
somewhat	O
similar	O
to	O
the	O
flying	B-Algorithm
ice	I-Algorithm
cube	I-Algorithm
problem	O
,	O
whereby	O
numerical	O
errors	O
in	O
handling	O
equipartition	O
of	O
energy	O
can	O
change	O
vibrational	O
energy	O
into	O
translational	O
energy	O
.	O
</s>
<s>
Energy	B-Algorithm
drift	I-Algorithm
-	O
usually	O
damping	O
-	O
is	O
substantial	O
for	O
numerical	B-Algorithm
integration	I-Algorithm
schemes	O
that	O
are	O
not	O
symplectic	B-Algorithm
,	O
such	O
as	O
the	O
Runge-Kutta	B-Algorithm
family	O
.	O
</s>
<s>
Symplectic	B-Algorithm
integrators	I-Algorithm
usually	O
used	O
in	O
molecular	O
dynamics	O
,	O
such	O
as	O
the	O
Verlet	B-Language
integrator	I-Language
family	O
,	O
exhibit	O
increases	O
in	O
energy	O
over	O
very	O
long	O
time	O
scales	O
,	O
though	O
the	O
error	O
remains	O
roughly	O
constant	O
.	O
</s>
<s>
The	O
energy	O
computed	O
from	O
the	O
modified	O
Hamiltonian	O
of	O
a	O
symplectic	B-Algorithm
integrator	I-Algorithm
is	O
from	O
the	O
true	O
Hamiltonian	O
.	O
</s>
<s>
Energy	B-Algorithm
drift	I-Algorithm
is	O
similar	O
to	O
parametric	O
resonance	O
in	O
that	O
a	O
finite	O
,	O
discrete	O
timestepping	O
scheme	O
will	O
result	O
in	O
nonphysical	O
,	O
limited	O
sampling	O
of	O
motions	O
with	O
frequencies	O
close	O
to	O
the	O
frequency	O
of	O
velocity	O
updates	O
.	O
</s>
<s>
The	O
fastest	O
motions	O
in	O
most	O
biomolecular	O
systems	O
involve	O
the	O
motions	O
of	O
hydrogen	O
atoms	O
;	O
it	O
is	O
thus	O
common	O
to	O
use	O
constraint	B-Algorithm
algorithms	I-Algorithm
to	O
restrict	O
hydrogen	O
motion	O
and	O
thus	O
increase	O
the	O
maximum	O
stable	O
time	O
step	O
that	O
can	O
be	O
used	O
in	O
the	O
simulation	O
.	O
</s>
<s>
Energy	B-Algorithm
drift	I-Algorithm
can	O
also	O
result	O
from	O
imperfections	O
in	O
evaluating	O
the	O
energy	O
function	O
,	O
usually	O
due	O
to	O
simulation	O
parameters	O
that	O
sacrifice	O
accuracy	O
for	O
computational	O
speed	O
.	O
</s>
<s>
Errors	O
in	O
the	O
system	O
being	O
simulated	O
can	O
also	O
induce	O
energy	B-Algorithm
drifts	I-Algorithm
characterized	O
as	O
"	O
explosive	O
"	O
that	O
are	O
not	O
artifacts	O
,	O
but	O
are	O
reflective	O
of	O
the	O
instability	O
of	O
the	O
initial	O
conditions	O
;	O
this	O
may	O
occur	O
when	O
the	O
system	O
has	O
not	O
been	O
subjected	O
to	O
sufficient	O
structural	O
minimization	O
before	O
beginning	O
production	O
dynamics	O
.	O
</s>
<s>
In	O
practice	O
,	O
energy	B-Algorithm
drift	I-Algorithm
may	O
be	O
measured	O
as	O
a	O
percent	O
increase	O
over	O
time	O
,	O
or	O
as	O
a	O
time	O
needed	O
to	O
add	O
a	O
given	O
amount	O
of	O
energy	O
to	O
the	O
system	O
.	O
</s>
<s>
The	O
practical	O
effects	O
of	O
energy	B-Algorithm
drift	I-Algorithm
depend	O
on	O
the	O
simulation	O
conditions	O
,	O
the	O
thermodynamic	O
ensemble	O
being	O
simulated	O
,	O
and	O
the	O
intended	O
use	O
of	O
the	O
simulation	O
under	O
study	O
;	O
for	O
example	O
,	O
energy	B-Algorithm
drift	I-Algorithm
has	O
much	O
more	O
severe	O
consequences	O
for	O
simulations	O
of	O
the	O
microcanonical	O
ensemble	O
than	O
the	O
canonical	O
ensemble	O
where	O
the	O
temperature	O
is	O
held	O
constant	O
.	O
</s>
<s>
However	O
,	O
it	O
has	O
been	O
shown	O
that	O
long	O
microcanonical	O
ensemble	O
simulations	O
can	O
be	O
performed	O
with	O
insignificant	O
energy	B-Algorithm
drift	I-Algorithm
,	O
including	O
those	O
of	O
flexible	O
molecules	O
which	O
incorporate	O
constraints	O
and	O
Ewald	O
summations	O
.	O
</s>
<s>
Energy	B-Algorithm
drift	I-Algorithm
is	O
often	O
used	O
as	O
a	O
measure	O
of	O
the	O
quality	O
of	O
the	O
simulation	O
,	O
and	O
has	O
been	O
proposed	O
as	O
one	O
quality	O
metric	O
to	O
be	O
routinely	O
reported	O
in	O
a	O
mass	O
repository	O
of	O
molecular	O
dynamics	O
trajectory	O
data	O
analogous	O
to	O
the	O
Protein	O
Data	O
Bank	O
.	O
</s>
