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We consider the dynamic large deviation behaviour of Kac's collisionalprocess for a range of initial conditions including equilibrium. We prove anupper bound with a rate function of the type which has previously been foundfor kinetic large deviation problems, and a matching lower bound restricted toa class of sufficiently good paths. However, we are able to show by an explicitcounterexample that the predicted rate function does not extend to a globallower bound: even though the particle system almost surely conserves energy,large deviation behaviour includes solutions to the Boltzmann equation which donot conserve energy, as found by Lu and Wennberg, and these occur strictly morerarely than predicted by the proposed rate function. At the level of theparticle system, this occurs because a macroscopic proportion of energy canconcentrate in $\mathfrak{o}(N)$ particles with probability$e^{-\mathcal{O}(N)}$.

Large Deviations of Kac's Conservative Particle System and Energy  Non-Conserving Solutions to the Boltzmann Equation: A Counterexample to the  Predicted Rate Function