Two phenomenological approaches are currently used in the study of the vitreous state. One is based on the concept of fictive temperature introduced by Tool [J. Res. Natl. Bur. Stand.34, 199 (1945)] and recently revisited by Nieuwenhuizen [Phys. Rev. Lett.80, 5580 (1998)]. The other is based on the thermodynamics of irreversible processes initiated by De Donder at the beginning of the last century [L’Affinité (Gauthier-Villars, Paris, 1927)] and recently used by Möller et al. for a thorough study of the glass transition [J. Chem. Phys.125, 094505 (2006)]. This latter approach leads to the possibility of describing the glass transition by means of the freezing-in of one or more order parameters connected to the internal structural degrees of freedom involved in the vitrification process. In this paper, the equivalence of the two preceding approaches is demonstrated, not only for glasses but in a very general way for any system undergoing an irreversible transformation. This equivalence allows the definition of an effective temperature for all systems departed from equilibrium generating a positive amount of entropy. In fact, the initial fictive temperature concept of Tool leads to the generalization of the notion of temperature for systems out of thermodynamic equilibrium, for which glasses are just particular cases.

1.
J.
Langer
,
Phys. Today
60
(
2
),
8
(
2007
).
2.
G. O.
Jones
and
F. E.
Simon
,
Endeavour
8
,
175
(
1949
) (in French).
3.
J. D.
Bernal
,
Trans. Faraday Soc.
33
,
27
(
1936
).
4.
R. O.
Davies
and
G. O.
Jones
,
Adv. Phys.
2
,
370
(
1953
).
5.
I.
Prigogine
and
R.
Defay
,
Thermodynamique Chimique, Nouvelle Redaction
(
Desoer
,
Liege
,
1950
), pp.
304
307
(in French).
6.
A. Q.
Tool
,
J. Res. Natl. Bur. Stand.
34
,
199
(
1945
).
8.
Y.
Yue
,
R.
von der Ohe
, and
S. L.
Jensen
,
J. Chem. Phys.
120
,
8053
(
2004
).
9.
10.
Th. M.
Nieuwenhuizen
,
Phys. Rev. Lett.
80
,
5580
(
1998
).
11.
Th. M.
Nieuwenhuizen
,
J. Phys. A
31
,
L201
(
1998
).
12.
Th. M.
Nieuwenhuizen
,
Phys. Rev. Lett.
79
,
1317
(
1997
).
13.
L. F.
Cugliandolo
,
J.
Kurchan
, and
L.
Peliti
,
Phys. Rev. E
55
,
3898
(
1997
).
14.
A.
Crisanti
and
F.
Ritort
,
J. Phys. A
36
,
R181
(
2003
).
15.
L. F.
Cugliandolo
,
Dynamics of Glassy Systems, Les Houches Session LXXVII, Slow Relaxation and Nonequilibrium Dynamics in Condensed Matter
(
Springer
,
Berlin
,
2003
), pp.
477
486
.
16.
J.
Casas-Vázquez
and
D.
Jou
,
Rep. Prog. Phys.
66
,
1937
(
2003
).
17.
M. L.
Roukes
,
M. R.
Freeman
,
R. S.
Germain
,
R. C.
Richardson
, and
M. B.
Ketchen
,
Phys. Rev. Lett.
55
,
422
(
1985
).
18.
M.
Meschke
,
W.
Guichard
, and
J.
Pekola
,
Nature (London)
444
,
187
(
2006
).
19.
J. C.
Mauro
,
P. K.
Gupta
, and
R. J.
Loucks
,
J. Chem. Phys.
126
,
184511
(
2007
).
20.
Th.
De Donder
,
L’Affinité
(
Gauthier-Villars
,
Paris
,
1927
) (in French).
21.
Th.
De Donder
,
L’Affinité, Rédaction Nouvelle
(
Gauthier-Villars
,
Paris
,
1936
) (in French).
22.
I.
Prigogine
,
Introduction à la Thermodynamique des Processus Irréversibles
(
Dunod
,
Paris
,
1968
) (in French).
23.
S. R.
De Groot
and
P.
Mazur
,
Non-Equilibrium Thermodynamics
(
Dover
,
New York
,
1984
).
24.
J. M.
Rubi
and
A.
Pérez-Madrid
,
Physica A
264
,
492
(
1999
).
25.
J. M. G.
Vilar
and
J. M.
Rubi
,
Proc. Natl. Acad. Sci. U.S.A.
98
,
11081
(
2001
).
26.
D.
Reguera
,
J. M.
Rubi
, and
J. M. G.
Vilar
,
J. Phys. Chem. B
109
,
21502
(
2005
).
27.
I.
Prigogine
and
R.
Defay
,
Thermodynamique Chimique (Conformément aux Methods de Gibbs et De Donder)
(
Desoer
,
Liege
,
1944
), Tome I;
ibid.
(
Desoer
,
Liege
,
1946
), Tome II (in French).
28.
N. L.
Ellegaard
,
T.
Christensen
,
P. V.
Christiansen
,
N. B.
Olsen
,
U. R.
Pedersen
,
T. B.
Schrøder
, and
J. C.
Dyre
,
J. Chem. Phys.
126
,
074502
(
2007
).
29.
J. W. P.
Schmelzer
and
I.
Gutzow
,
J. Chem. Phys.
125
,
184511
(
2006
).
30.
J.
Jäckle
,
Rep. Prog. Phys.
49
,
171
(
1986
).
31.
C. A.
Angell
,
K. L.
Ngai
,
G. B.
McKenna
,
P. F.
McMillan
, and
S. W.
Martin
,
J. Appl. Phys.
88
,
3113
(
2000
).
32.
G. B.
McKenna
,
Comprehensive Polymer Science
, edited by
C.
Booth
and
C.
Price
(
Pergamon
,
Oxford
,
1989
), Vol.
2
, pp.
311
362
.
33.
G. B.
McKenna
and
S. L.
Simon
,
Handbook of Thermal Analysis and Calorimetry
, edited by
S. Z. D.
Cheng
(
Elsevier
,
Amsterdam
,
2002
), Vol.
3
, pp.
49
109
.
34.
I. C.
Dyre
,
Rev. Mod. Phys.
78
,
953
(
2006
).
35.
Y. Z.
Yue
,
J. de C.
Christiansen
, and
S. L.
Jensen
,
Chem. Phys. Lett.
357
,
20
(
2002
).
36.
Th. M.
Nieuwenhuizen
,
Phys. Rev. E
61
,
267
(
2000
).
37.
Th. M.
Nieuwenhuizen
,
J. Phys.: Condens. Matter
12
,
6543
(
2000
).
38.
Th. M.
Nieuwenhuizen
,
J. Chem. Phys.
115
,
8083
(
2001
).
39.
40.
41.
J.
Möller
,
I.
Gutzow
, and
J. W. P.
Schmelzer
,
J. Chem. Phys.
125
,
094505
(
2006
).
42.
C. A.
Angell
,
J. Therm Anal. Calorim.
69
,
785
(
2002
).
43.
I.
Prigogine
and
P.
Mazur
,
Physica (Amsterdam)
18
,
241
(
1953
).
44.
N. O.
Birge
and
S. R.
Nagel
,
Phys. Rev. Lett.
54
,
2674
(
1985
).
45.
N. O.
Birge
,
Phys. Rev. B
34
,
1631
(
1986
).
46.
N. O.
Birge
and
S. R.
Nagel
,
Rev. Sci. Instrum.
58
,
1464
(
1987
).
47.
S.
Weyer
,
M.
Merzlyakov
, and
C.
Schick
,
Thermochim. Acta
377
,
85
(
2001
).
48.
K.
Ema
and
H.
Yao
,
Thermochim. Acta
304/305
,
157
(
1997
).
49.
J.-L.
Garden
,
E.
Château
, and
J.
Chaussy
,
Appl. Phys. Lett.
84
,
3597
(
2004
).
50.
O.
Bourgeois
,
S.
Skipetrov
,
F.
Ong
, and
J.
Chaussy
,
Phys. Rev. Lett.
94
,
057007
(
2005
).
51.
H.
Baur
and
B.
Wunderlich
,
J. Therm Anal. Calorim.
54
,
437
(
1998
).
52.
J.-L.
Garden
,
Thermochim. Acta
452
,
85
(
2007
).
53.
Y. H.
Jeong
,
Thermochim. Acta
304/305
,
67
(
1997
).
54.
J.-L.
Garden
,
Thermochim. Acta
460
,
85
(
2007
).
55.
J.-L.
Garden
and
J.
Richard
,
Thermochim. Acta
461
,
57
(
2007
).
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