What is the difference between fictive temperature and transition temperature of glass?
To my knowledge, the concept of fictive temperature (Tf) was introduced by Tool ( http://onlinelibrary.wiley.com/doi/10.1111/j.1151-2916.1946.tb11592.x/abstract ). I would suggest to understand it as follows: In the metastable liquid above the (thermal) glass transition range Tf equals the actual temperature Tf=T. Appropriate structural relaxation time (tau) - to reach a (metastable) equilibrium configuration - is a function of temperature (T) and structural state (Tf) of the material: tau(T,Tf). During cooling with a certain rate (q), the mobility of the atoms or molecules strongly decreases (Tf>T) and the (thermal) glass transition occurs if the structural relaxation time exceeds the reciprocal cooling rate tau(T,Tf)>a/q (for a=1K, so called Frenkel-Kobeko-Reiner equation). If the temperature now further decreases, the structure "freezes" and is therefore "trapped" in a definite configurational state at the limit of the fictive temperature Tf'(q). Mostly, this temperature is simply called fictive temperature and it is used synonymously as glass transition temperature. However, the glass transition temperature Tg is also a material property defined at the temperature @ viscosity eta = 10^12 Pa*s. I hope, my explanation is useful for you.
Tg is a material-specific quantity, conventionally defined kinetically at the temperature where viscosity of the liquids approaches 10^12 Pa-s as mentioned by Norman, or, alternatively, defined thermodynamically at the temperature where heat capacity / thermal expansion coefficient abruptly jumps between liquids and glasses. Fictive temperatures Tf is a function of real temperature T [Tf = T for the case of T>Tg (liquid, preferentially supercooled liquid), and Tf>T for the case of T
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