  Nanomechanical responses (force-time profiles) of crystal lattices under
deformation exhibit random critical jumps, reflecting the underlying structural
transition processes. Despite extensive data collection, interpreting dynamic
critical responses and their underlying mechanisms remains a significant
challenge. This study explores a microscopic theoretical approach to analyse
critical force fluctuations in martensitic transitions. Extensive sampling of
the critical forces was performed using nonequilibrium molecular dynamics
simulations of an atomic model of single-crystalline titanium nickel. We
demonstrate that a framework of nonequilibrium statistical mechanics offers a
principled explanation of the relationship between strain rate and the critical
force distribution as well as its mean. The martensitic transition is
represented on a free energy landscape, taking into account the thermally
activated evolution of atomic arrangements over a barrier during its
time-dependent deformation. The framework enables consistent inference of the
relevant fundamental properties (e.g., intrinsic rate, activation free energy)
that define the rate process of structural transition. The study demonstrates
how the statistical characterisation of nanomechanical response-stimulus
patterns can offer microscopic insights into the deformation behaviours of
crystalline materials.
