Thermodynamic description of the glassy state
In the fifties, sixties and seventies of last century quite some effort was devoted to
find a thermodynamic description of the glassy state. The efforts failed on the experimental
test of the so-called Ehrenfest relations. The resulting Prigogine-defay ratio should be equal
to unity in the considered theories, while experimental values were typically between 2 and 5.
[L27] draws attention to unexpected behavior of the dynamical transition of the so-called
p-spin model. In [L30] the analysis of the so-called marginal state of the p-spin model showed
that a two-temperature approach worked in the dynamical regime.
The letter [L31] explains how the old paradox of Ehrenfest relations and Prigogine-Defay ratio
gets resolved in this two-temperature - two-entropy approach.
This all became more clear in [L32] and [P49], where systems having two sets of modes are considered:
fast ones that are just in equilibrium with the bath (not yet taken into account there) and slow ones,
so slow that they set out their own equilibrium at an effective temperature that depends slowly on time.
The associated variable to the effective temperature is the configurational entropy, here in the
definition of entropy of slow modes. The time-dependencies are such that previous assumptions of
being near to equilibrium are not well enough satisfied, and, as a result, the Prigogine-Defay ratio
can take any value, even negative.
A richer model, in which all these and other standard glassy properties are included, [I4], was
worked out in great detail by my PhD student Luca Leuzzi, [P53] and [P57].
Several of these aspects became apparant in an exactly solvable model for a model glass, [L29].
A pedagogic paper on this field is [P56].
In [N1] en [N2] geef ik een beschrijving in het Nederlands Tijdschrift voor Natuurkunde.
Book
Luca Leuzzi and Theo M. Nieuwenhuizen,[P60] L. Leuzzi and Th.M. N., Exactly solvable model glass with facilitated dynamics, J. Phys. Cond. Mat. 14 (2002) 1637-1649
[P57] Luca
Leuzzi and Theo M. N., Inherent Structures in models for fragile and strong
glass, Phys. Rev. E 64, 066125
(2001) (15 pages) [P56] Th.M.
N., Formulation of thermodynamics for the glassy state: configurational
energy as a modest source of energy, J. Chem. Phys. 115 8083-8088 (2001) [P53] Luca
Leuzzi and Th. M. N., Effective temperatures in an exactly solvable model
for a fragile glass, Phys.
Rev. E 64, 011508 (2001) (24 pages) [P50] A.E.
Allahverdyan, Th.M. N., and D.B. Saakian, Model glasses coupled to two
different heat baths, Eur. Phys. J. B 16 (2000) 317-355 [P49] Th.M.
N., Thermodynamic picture of the glassy state gained from exactly solvable
models, Phys.
Rev. E 61 (2000) 267-292 [I4]
Th.M. N., Solvable model for the standard folklore of the glassy state,
cond-mat/9911052 [L32] Th.M.
N., Thermodynamics of the glassy state: effective temperature as an additional
system parameter, Phys.
Rev. Lett. 80 (1998) 5580-5583 [L31] Th.M.
N., Ehrenfest relations at the glass transition: solution to an old paradox,
Phys.
Rev. Lett. 79 (1997) 1317-1320
[L30] Th.M.
N., Thermodynamic description of a dynamical glassy transition, J.
Phys. A Lett. 31 (1998) L201-L207 [L29] Th.M.
N., Solvable glassy system: static versus dynamical transition, Phys.
Rev. Lett. 78 (1997) 3491-3494 [L27] Th.M.
N., To maximize or not to maximize the free energy of glassy systems,
Phys.
Rev. Lett 74 (1995) 3463-3466