jats:titleAbstract</jats:title> jats:pWe present a minimal Landau theory of plastic-to-crystal phase transitions in which the key components are a multipole-moment order parameter that describes the orientational ordering of the constituent molecules, coupling between such order parameter and elastic strains, and thermal expansion. We illustrate the theory with the simplest non-trivial model in which the orientational ordering is described by a quadrupole moment, and use such model to calculate barocaloric effects in plastic crystals that are driven by hydrostatic pressure. The model captures characteristic features of plastic-to-crystal phase transitions, namely large changes in volume and entropy at the transition, as well as the linear dependence of the transition temperature with pressure. We identify temperature regions in the barocaloric response associated with the individual plastic and crystal phases, and those involving the phase transition. Our model is in overall agreement with previous experiments in powdered samples of fullerite Cjats:sub60</jats:sub>, and predicts peak isothermal entropy changes of jats:inline-formula jats:tex-math/ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mrow mml:mrow mml:mo∼</mml:mo> </mml:mrow> mml:mn90</mml:mn> <mml:mstyle scriptlevel="0"/> mml:mrow <mml:mi mathvariant="normal">J</mml:mi> mml:msup <mml:mi mathvariant="normal">K</mml:mi> mml:mrow mml:mo−</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:msup> mml:msup mml:mikg</mml:mi> mml:mrow mml:mo−</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> </jats:inline-formula> and peak adiabatic temperature changes of jats:inline-formula jats:tex-math/ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mrow mml:mrow mml:mo∼</mml:mo> </mml:mrow> mml:mn35</mml:mn> <mml:mstyle scriptlevel="0"/> mml:mrow <mml:mi mathvariant="normal">K</mml:mi> </mml:mrow> </mml:mrow> </mml:math> </jats:inline-formula> under jats:inline-formula jats:tex-math/ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mrow mml:mn0.60</mml:mn> <mml:mstyle scriptlevel="0"/> </mml:mrow> </mml:math> </jats:inline-formula>GPa at jats:inline-formula jats:tex-math/ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mrow mml:mn265</mml:mn> <mml:mstyle scriptlevel="0"/> </mml:mrow> </mml:math> </jats:inline-formula>K in fullerite single crystals.</jats:p>