The effects of particle size (2-6 nm) and temperature (300-2700 K) on the stability and local structural evolutions of amorphous equiatomic FePt bulk/nanoalloys have been investigated by combining Embedded Atom Model (EAM) with classical molecular dynamics (MD) simulation method. The three dimensional (3D) atomic configuration of amorphous FePt NPs by means of Voronoi analysis reveals that, deformed bcc (d-bcc) and icosahedron (d-ico) type structures are most probable local atomic configurations for 2-6 nm sized Fe50Pt50 NPs both in liquid (1700 K) and glassy (300 K) states. It was shown that nano-scale phase separation takes place around 300 K for 2 nm sized FePt NPs that leads to formation of spherical core-shell segregated structure having Pt-Fe-rich core and Fe-rich surface. Compared to core region, more ordered and high dense configuration of atoms at the surface gives rise to decrease in surface entropy of NPs and hence bringing about surface energy anomaly with positive temperature coefficient above the glass transition temperatures. Below glass transition temperatures of the FePt nanoalloy particles, the thermodynamically stable amorphous phase (TSA) would appear. Glass transition temperature of amorphous Fe50Pt50 NPs increases with increasing particle size and eventually approaches to the glass temperature of bulk system for NPs diameters >= similar to 16 nm. Results of current predictions are in good qualitative and semi-quantitative agreement with other theoretical and experimental findings reported in the literature. (C) 2019 Elsevier B.V. All rights reserved.