Two problems pertaining to solid-solid phase transitions are presented here.First, we conduct Langevin dynamics calculations on a chain of masses and bistable springs in a viscous fluid, and extract a temperature dependent kinetic relation by observing that the dissipation at a phase boundary can be estimated by performing an energy balance. Using this kinetic relation we solve boundary value problems for a bistable bar immersed in a constant temperature bath and show that the resultant force-extension relation matches very well with the Langevin dynamics results. We estimate the force fluctuations at the pulled end of the bar due to thermal kicks from the bath by using a partition function. We also show rate dependence of hysteresis in cyclic loading of the bar arising from the stick-slip kinetics. we also extract equilibrium and non-equilibrium information from an over-damped Langevin system using fluctuation theorems. Second, we use a double-well stored energy function in a chemo-elastic model of gels to capture the existence of two phases of the network. We model cyclic compression/decompression experiments on fibrous gels and show that they exhibit propagating interfaces and hysteretic stress-strain curves that have been observed in experiments. We can capture features in the rate-dependent response of these fibrous gels without recourse to finite element calculations. We also use the model to study the rheological behavior of fibrous gels. We obtain the storage and loss modulus of fibrous gels by performing small amplitude oscillatory compression around various levels of deformation.