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The Shapere-Wilczek model \cite{wil}, or so called $ fgh$ model, enjoys theremarkable features of a Time Crystal (TC) that has a non-trivial timedependence in its lowest energy state (or the classical ground state). Weconstruct a particular form of $ fgh$ model (with specified $f,g,h$ functions)that is derived from a Mini-superspace version of a quadratic $f(R,R_{\mu\nu})$gravity theory. Main part of the investigation deals with thermodynamicproperties of such systems from classical statistical mechanics perspective.Our analysis reveals the possibility of a {\it phase transition}. Because ofthe higher (time) derivative nature of the model computation of the partialfunction is non-trivial and requires newly discovered techniques. We speculateabout possible connection between our model and the Multiverse scenario.

Thermodynamics and Phase Transition in Shapere-Wilczek {\it fgh} model: Cosmological Time Crystal in Quadratic Gravity