%0 Book Section %1 statphys23_0654 %A Ilg, P. %A Barrat, J.L. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K activated amorphous dynamics effective flow nonequilibrium shear state stationary statphys23 system temperature topic-3 %T Thermal versus driven activation dynamics in sheared glassy systems %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=654 %X Activated events, as described by the theories of Eyring and Kramers, lie at the heart of many descriptions of dynamical processes in condensed matter, chemical physics or materials science. The essential result can be summarized in the celebrated Arrhenius formula, relating the rate $r$ of the process to the energy barrier $\Delta E$ and the temperature $T$, $r \exp(-\Delta E/ k_BT)$. The notion of thermodynamic temperature becomes problematic in systems that are in a nonequilibrium state, e.g.~under the influence of an external driving force. A prototypical example is that of a glassy system undergoing a steady shear deformation at constant shear rate, which brings the system into a nonequilibrium, stationary state. In such driven systems, the concept of an effective temperature $T_eff$ has become increasingly popular in the recent years, either in the form of a phenomenological parameter that quantifies the distance to equilibrium, or in more formal approaches that make use of the fluctuation-dissipation ratio. A natural question arises, as to whether the effective temperature concept for such systems can be extended to the description of rate processes in nonequilibrium systems. A natural extension of the Arrhenius formula would be to rewrite it as $r\sim \exp(-\Delta E/ k_BT_eff)$. In this work, we use numerical simulations of a simple model to investigate the validity of such an extension, which we describe as 'driven activation'. Our results show that the external driving force has a strong influence on the barrier rate crossing of an activated system weakly coupled to the nonequilibrium system. This influence can be quantified by introducing in the Arrhenius expression an effective temperature, which is close to the one determined from the fluctuation dissipation relation.

@incollection{statphys23_0654, abstract = {Activated events, as described by the theories of Eyring and Kramers, lie at the heart of many descriptions of dynamical processes in condensed matter, chemical physics or materials science. The essential result can be summarized in the celebrated Arrhenius formula, relating the rate $r$ of the process to the energy barrier $\Delta E$ and the temperature $T$, $r \sim \exp(-\Delta E/ k_BT)$. The notion of thermodynamic temperature becomes problematic in systems that are in a nonequilibrium state, e.g.~under the influence of an external driving force. A prototypical example is that of a glassy system undergoing a steady shear deformation at constant shear rate, which brings the system into a nonequilibrium, stationary state. In such driven systems, the concept of an effective temperature $T_\mathrm{eff}$ has become increasingly popular in the recent years, either in the form of a phenomenological parameter that quantifies the distance to equilibrium, or in more formal approaches that make use of the fluctuation-dissipation ratio. A natural question arises, as to whether the effective temperature concept for such systems can be extended to the description of rate processes in nonequilibrium systems. A natural extension of the Arrhenius formula would be to rewrite it as $r\sim \exp(-\Delta E/ k_BT_\mathrm{eff})$. In this work, we use numerical simulations of a simple model to investigate the validity of such an extension, which we describe as 'driven activation'. Our results show that the external driving force has a strong influence on the barrier rate crossing of an activated system weakly coupled to the nonequilibrium system. This influence can be quantified by introducing in the Arrhenius expression an effective temperature, which is close to the one determined from the fluctuation dissipation relation.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Ilg, P. and Barrat, J.L.}, biburl = {https://www.bibsonomy.org/bibtex/24da5e11be6d25a60e46ce4b3433e016f/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {aab71fd014400c073b1a2efa0d85f66e}, intrahash = {4da5e11be6d25a60e46ce4b3433e016f}, keywords = {activated amorphous dynamics effective flow nonequilibrium shear state stationary statphys23 system temperature topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:26.000+0200}, title = {Thermal versus driven activation dynamics in sheared glassy systems}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=654}, year = 2007 }