The Negative Dimensional Oscillator at Finite Temperature

We study the thermal behavior of the negative dimensional harmonic oscillator of Dunne and Halliday that at zero temperature, due to a hidden BRST symmetry of the classical harmonic oscillator, is shown to be equivalent to the Grassmann oscillator of Finkelstein and Villasante. At finite temperature we verify that although being described by Grassmann numbers the thermal behavior of the negative dimensional oscillator is quite different from a Fermi system.