Space-time thermodynamics of the glass transition.

We consider the probability distribution for fluctuations in dynamical action and similar quantities related to dynamic heterogeneity. We argue that the so-called "glass transition" is a manifestation of low action tails in these distributions where the entropy of trajectory space is subextensive in time. These low action tails are a consequence of dynamic heterogeneity and an indication of phase coexistence in trajectory space. The glass transition, where the system falls out of equilibrium, is then an order-disorder phenomenon in space-time occurring at a temperature T(g), which is a weak function of measurement time. We illustrate our perspective ideas with facilitated lattice models and note how these ideas apply more generally.

[1]  Berend Smit,et al.  Understanding Molecular Simulation , 2001 .

[2]  M. Sellitto,et al.  Out-of-equilibrium dynamical fluctuations in glassy systems. , 2004, The Journal of chemical physics.

[3]  Glenn H. Fredrickson,et al.  Kinetic Ising model of the glass transition , 1984 .

[4]  Zohar Nussinov,et al.  A thermodynamic theory of supercooled liquids , 1995 .

[5]  David Chandler,et al.  Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems. , 2002, Physical review letters.

[6]  David Chandler,et al.  Transition path sampling: throwing ropes over rough mountain passes, in the dark. , 2002, Annual review of physical chemistry.

[7]  Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Geometrical picture of dynamical facilitation , 2004, cond-mat/0401551.

[9]  Pablo G. Debenedetti,et al.  Supercooled liquids and the glass transition , 2001, Nature.

[10]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[11]  J. Jäckle,et al.  A hierarchically constrained kinetic Ising model , 1991 .

[12]  G. Biroli,et al.  On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses. , 2004, Journal of Chemical Physics.

[13]  R. Richert.  Heterogeneous dynamics in liquids: fluctuations in space and time , 2002 .

[14]  M D Ediger,et al.  Spatially heterogeneous dynamics in supercooled liquids. , 2003, Annual review of physical chemistry.

[15]  C. Angell,et al.  Formation of Glasses from Liquids and Biopolymers , 1995, Science.

[16]  Giorgio Parisi,et al.  On non-linear susceptibility in supercooled liquids , 2000, cond-mat/0005095.

[18]  Dynamic criticality in glass-forming liquids. , 2003, Physical review letters.

[19]  F. Guerra.  Spin Glasses , 2005, cond-mat/0507581.

[20]  J Kurchan,et al.  Metastable states in glassy systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  J. P. Garrahan,et al.  Coarse-grained microscopic model of glass formers , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[22]  P G Wolynes,et al.  Fragilities of liquids predicted from the random first order transition theory of glasses. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Christensen,et al.  Universal fluctuations in correlated systems , 1999, Physical review letters.

[24]  S. Glotzer.  Spatially heterogeneous dynamics in liquids: insights from simulation , 2000 .

[25]  S. Nagel,et al.  Supercooled Liquids and Glasses , 1996 .

[26]  G. Biroli,et al.  Dynamical susceptibility of glass formers: contrasting the predictions of theoretical scenarios. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Peter Sollich,et al.  Glassy dynamics of kinetically constrained models , 2002, cond-mat/0210382.

[28]  Hugo Bissig,et al.  Time-resolved correlation: a new tool for studying temporally heterogeneous dynamics , 2003 .

[29]  A. B. Bortz,et al.  A new algorithm for Monte Carlo simulation of Ising spin systems , 1975 .