The lack of a reliable method to evaluate the convergence of molecular dynamics simulations has contributed to discrepancies in different areas of molecular dynamics. In the present work, the method of information entropy is introduced to molecular dynamics for stationarity assessment. The Shannon information entropy formalism is used to monitor the convergence of the atom motion to a steady state in a continuous spatial domain and is also used to assess the stationarity of calculated multidimensional fields such as the temperature field in a discrete spatial domain. It is demonstrated in this work that monitoring the information entropy of the atom position matrix provides a clear indicator of reaching steady state in radiation damage simulations, non-equilibrium molecular dynamics thermal conductivity computations, and simulations of Poiseuille and Couette flow in nanochannels. A main advantage of the present technique is that it is non-local and relies on fundamental quantities available in all molecular dynamics simulations. Unlike monitoring average temperature, the technique is applicable to simulations that conserve total energy such as reverse non-equilibrium molecular dynamics thermal conductivity computations and to simulations where energy dissipates through a boundary as in radiation damage simulations. The method is applied to simulations of iron using the Tersoff/ZBL splined potential, silicon using the Stillinger–Weber potential, and to Lennard–Jones fluid. Its applicability to both solids and fluids shows that the technique has potential for generalization to other areas in molecular dynamics.

1.
H. A.
Scheraga
,
M.
Khalili
, and
A.
Liwo
,
Annu. Rev. Phys. Chem.
58
,
57
(
2007
).
2.
3.
M. S.
El-Genk
,
K.
Talaat
, and
B. J.
Cowen
,
J. Appl. Phys.
123
,
205104
(
2018
).
4.
X. W.
Zhou
,
S.
Aubry
,
R. E.
Jones
,
A.
Greenstein
, and
P. K.
Schelling
,
Phys. Rev. B
79
,
115201
(
2009
).
5.
P. C.
Howell
,
J. Chem. Phys.
137
,
224111
(
2012
).
6.
D. P.
Sellan
,
E. S.
Landry
,
J. E.
Turney
,
A. J. H.
McGaughey
, and
C. H.
Amon
,
Phys. Rev. B
81
,
214305
(
2010
).
7.
B. J.
Cowen
and
M. S.
El-Genk
,
Model. Simul. Mater. Sci. Eng.
25
,
085009
(
2017
).
8.
B. J.
Cowen
and
M. S.
El-Genk
,
Model. Simul. Mater. Sci. Eng.
26
,
085005
(
2018
).
9.
P. K.
Schelling
,
S. R.
Phillpot
, and
P.
Keblinski
,
Phys. Rev. B
65
,
144306
(
2002
).
10.
A.
Grossfield
,
S. E.
Feller
, and
M. C.
Pitman
,
Proteins Struct. Funct. Bioinform.
67
,
31
(
2007
).
11.
B.
Knapp
,
S.
Frantal
,
M.
Cibena
,
W.
Schreiner
, and
P.
Bauer
,
J. Comput. Biol.
18
,
997
(
2011
).
12.
C.
Abs da Cruz
,
K.
Termentzidis
,
P.
Chantrenne
, and
X.
Kleber
,
J. Appl. Phys.
110
,
034309
(
2011
).
13.
H.
Zaoui
,
P. L.
Palla
,
F.
Cleri
, and
E.
Lampin
,
Phys. Rev. B
94
,
054304
(
2016
).
14.
C. J.
Glassbrenner
and
G. A.
Slack
,
Phys. Rev.
134
,
A1058
(
1964
).
15.
M. S.
Green
,
J. Chem. Phys.
22
,
398
(
1954
).
16.
R.
Kubo
,
M.
Yokota
, and
S.
Nakajima
,
J. Phys. Soc. Jpn.
12
,
1203
(
1957
).
17.
T.
Ikeshoji
and
B.
Hafskjold
,
Mol. Phys.
81
,
251
(
1994
).
18.
F.
Müller-Plathe
,
J. Chem. Phys.
106
,
6082
(
1997
).
19.
E.
Lampin
,
P. L.
Palla
,
P.-A.
Francioso
, and
F.
Cleri
,
J. Appl. Phys.
114
,
033525
(
2013
).
20.
H.
Dong
,
Z.
Fan
,
L.
Shi
,
A.
Harju
, and
T.
Ala-Nissila
,
Phys. Rev. B
97
,
094305
(
2018
).
21.
K.
Nordlund
,
S. J.
Zinkle
,
A. E.
Sand
,
F.
Granberg
,
R. S.
Averback
,
R. E.
Stoller
,
T.
Suzudo
,
L.
Malerba
,
F.
Banhart
,
W. J.
Weber
,
F.
Willaime
,
S. L.
Dudarev
, and
D.
Simeone
,
J. Nucl. Mater.
512
,
450
(
2018
).
22.
E. Y.
Chen
,
C.
Deo
, and
R.
Dingreville
,
J. Phys. Condens. Matter
32
,
045402
(
2020
).
23.
T.
Goorley
,
M.
James
,
T.
Booth
,
F.
Brown
,
J.
Bull
,
L. J.
Cox
,
J.
Durkee
,
J.
Elson
,
M.
Fensin
,
R. A.
Forster
,
J.
Hendricks
,
H. G.
Hughes
,
R.
Johns
,
B.
Kiedrowski
,
R.
Martz
,
S.
Mashnik
,
G.
McKinney
,
D.
Pelowitz
,
R.
Prael
,
J.
Sweezy
,
L.
Waters
,
T.
Wilcox
, and
T.
Zukaitis
,
Nucl. Technol.
180
,
298
(
2012
).
24.
V.
Şeker
and
Ü
Çolak
,
Nucl. Eng. Des.
222
,
263
(
2003
).
25.
Ü
Çolak
and
V.
Seker
,
Nucl. Sci. Eng.
149
,
131
(
2005
).
26.
K.
Talaat
,
J.
Xi
,
P.
Baldez
, and
A.
Hecht
,
Sci. Rep.
9
,
17450
(
2019
).
27.
J.
Cheatham
and
F.
Brown
, LA-UR-06-5886,
2006
.
28.
C. E.
Shannon
,
Bell Syst. Tech. J.
27
,
379
(
1948
).
29.
F. B.
Brown
, in PHYSOR-2006—American Nuclear Society Topical Meeting on Reactor Physics (American Nuclear Society,
2006
).
30.
T.
Ueki
and
F. B.
Brown
, in American Nuclear Society Winter Meeting (American Nuclear Society,
2002
).
31.
F.
Brown
,
B.
Nease
, and
J.
Cheatham
, in Joint International Topical Meeting Mathematics and Computations and Supercomputing in Nuclear Applications M C + SNA 2007 (American Nuclear Society,
2007
).
32.
P. K.
Romano
and
B.
Forget
,
Ann. Nucl. Energy
51
,
274
(
2013
).
33.
O. A.
Olvera-Guerrero
,
A.
Prieto-Guerrero
, and
G.
Espinosa-Paredes
,
Ann. Nucl. Energy
108
,
1
(
2017
).
34.
O. A.
Olvera-Guerrero
,
A.
Prieto-Guerrero
, and
G.
Espinosa-Paredes
,
Entropy
19
,
359
(
2017
).
35.
S.
Rass
,
D.
Schuller
, and
C.
Kollmitzer
,
Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
(Springer,
2010
), pp.
166
177
.
36.
M.
Bansal
and
M.
Hanmandlu
,
J. Electr. Syst. Inf. Technol.
4
,
135
(
2017
).
37.
M. A.
Aljanabi
,
Z. M.
Hussain
, and
S. F.
Lu
,
Math. Probl. Eng.
2018
,
1
(
2018
).
38.
J. D.
Chodera
,
J. Chem. Theory Comput.
12
,
1799
(
2016
).
39.
J.
Byggmästar
and
F.
Granberg
,
J. Nucl. Mater.
528
,
151893
(
2020
).
40.
F. H.
Stillinger
and
T. A.
Weber
,
Phys. Rev. B
31
,
5262
(
1985
).
41.
M.
Misiti
,
Y.
Misiti
,
G.
Oppenheim
, and
J.-M.
Poggi
,
Matlab Wavelet Toolbox User’s Guide. Version 3
(MathWorks,
2004
).
42.
G.
Nason
,
Wavelet Methods in Statistics with R
(Springer,
2008
) [ISBN 978-0-387-75961-6].
43.
S.
Plimpton
,
J. Comput. Phys.
117
,
1
(
1995
).
44.
M. P.
Allen
and
D. J.
Tildesley
, Computer Simulation of Liquids (
Oxford University Press
,
1989
).
45.
J. J.
Morales
,
M. J.
Nuevo
, and
L. F.
Rull
,
J. Comput. Phys.
89
,
432
(
1990
).
46.
T. P.
Straatsma
,
H. J. C.
Berendsen
, and
A. J.
Stam
,
Mol. Phys.
57
,
89
(
1986
).
47.
J.
Kaiser
,
T.
Feng
,
J.
Maassen
,
X.
Wang
,
X.
Ruan
, and
M.
Lundstrom
,
J. Appl. Phys.
121
,
044302
(
2017
).
48.
H. A. K.
Rady
,
Egypt. Inform. J.
12
,
197
(
2011
).
49.
J.
le Page
,
D. R.
Mason
,
C. P.
Race
, and
W. M. C.
Foulkes
,
New J. Phys.
11
,
013004
(
2009
).
50.
K.
Talaat
,
R.
Das
,
B.
Romero
,
C.
Cakez
,
O.
Anderoglu
,
S.
Lee
,
Y.
Lee
,
H.
Ban
,
K.
Woloshun
,
S. J.
Kim
,
D.
Rao
, and
C.
Unal
, in
18th International Topical Meeting on Nuclear Reactor and Thermal Hydraulics NURETH 2019
(American Nuclear Society,
2019
).
You do not currently have access to this content.