  The elastocaloric effect (ECE) is a thermodynamic quantity relating changes
in entropy to changes in strain experienced by a material. As such, ECE
measurements can provide valuable information about the entropy landscape
proximate to strain-tuned phase transitions. For ordered states that break only
point symmetries, bilinear coupling of the order parameter with strain implies
that the ECE can also provide a window on fluctuations above the critical
temperature, and hence, in principle, can also provide a thermodynamic measure
of the associated susceptibility. To demonstrate this, we use the ECE to
sensitively reveal the presence of nematic fluctuations in the archetypal
Fe-based superconductor Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$. By performing these
measurements simultaneously with elastoresistivity in a multimodal fashion, we
are able to make a direct and unambiguous comparison of these closely related
thermodynamic and transport properties, both of which are sensitive to nematic
fluctuations. As a result, we have uncovered an unanticipated doping-dependence
of the nemato-elastic coupling and of the magnitude of the scattering of low
energy quasi-particles by nematic fluctuations -- while the former weakens, the
latter increases dramatically with increasing doping.
