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 $T$,
$r \exp(-\Delta E/ k_BT)$.
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.
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