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Using Ba(Fe$_{0.975}$Co$_{0.025}$)$_2$As$_{2}$ as an exemplar materialexhibiting second order electronic-nematic and antiferromagnetic transitions,we present measurements that reveal anomalies in the elastoresistance$\left(\frac{\partial \rho_{ij}}{\partial\varepsilon_{kl}}\right)$ andelastocaloric effect $\left(\frac{\partial T}{\partial\varepsilon_{kl}}\right)$at both phase transitions. Both effects are understood to arise from the effectof strain on the transition temperatures; in the region close to the phasetransitions this leads to (1) similarity between the strain and temperaturederivatives of the resistivity and (2) similarity between the elastocaloriceffect and the singular part of the specific heat. These mechanisms forelastoresistance and elastocaloric effect should be anticipated for anymaterial in which mechanical deformation changes the transition temperature.Furthermore, these measurements provide evidence that the Fisher-Langerrelation $\rho^{(c)} \propto U^{(c)}$ between the scattering from criticaldegrees of freedom and their energy-density, respectively, holds near each ofthe Ne\'{e}l and electronic nematic transitions in the material studied.

Elastoresistive and Elastocaloric Anomalies at Magnetic and Electronic-Nematic Critical Points