FIZIKA B 7 (1998) 4, 235-242
MODIFICATION OF THE DEBYE THEORY OF SPECIFIC HEAT DUE TO NON-EXTENSIVE
Department of Physics, Massachussetts College of Liberal Arts, North
MA 01247, U. S. A.
Received 21 December 1998; Accepted 6 April 1999
By allowing for a multi-fractal distribution for the population densities of the states
of a harmonic oscillator we demostrate that the thermal average energy of a quantizied
harmonic oscillator receives a correction due to the non-extensive statistics of Tsallis.
By applying this result to the phonon spectrum we show that this in turn generates an
anomalous correction to the Debye formula for the specific heat of a solid at low
PACS numbers: 05.30.-d, 63.70.+h, 65.40.-f
Keywords: non-extensive statistics of Tsallis, multi-fractal distribution densities of the
states, quantizied harmonic oscillator, specific heat of a solid, anomalous correction to
the Debye formula