  We address the issue of stock market fluctuations within Langevin Dynamics
(LD) and the thermodynamics definitions of multifractality in order to study
its second-order characterization given by the analogous specific heat C_{q},
where q is an analogous temperature relating the moments of the generating
partition function for the financial data signals. Due to non-linear and
additive noise terms within the LD, we found that C_{q} can display a shoulder
to the right of its main peak as also found in the S&P500 historical data which
may resemble a classical phase transition at a critical point.
