We propose a radically novel approach to analyze speech signals from a statistical physics perspective. Our approach is based on a new framework, the Microcanonical Multiscale Formalism (MMF), which is based on the computation of singularity exponents, defined at each point in the signal domain. The latter allows nonlinear analysis of complex dynamics and, particularly, characterizes the intermittent signature. We study the validity of the MMF for the speech signal and show that singularity exponents convey indeed valuable information about its local dynamics. We define an accumulative measure on the exponents which reveals phoneme boundaries as the breaking points of a piecewise linear-like curve. We then develop a simple automatic phonetic segmentation algorithm using piecewise linear curve fitting. We present experiments on the full TIMIT database. The results show that our algorithm yields considerably better accuracy than recently published ones.