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tokens: et al. 1988 ) applied to IST EoS of quantum gases (see Bugaev et al. 2017 for details). This allows us not only to reproduce the properties of the normal nuclear matter but also to significantly extend the range of IST EoS applicability. The goal of this work is to study the constraints that can possibly be imposed on the IST EoS from the astrophysical observational data of NSs. This is necessary to find which set of parameters of this EoS simultaneously fits the experimental data from the A+A collisions and the astrophysical observations on NSs. The paper is organized as follows. In Section 2 we briefly review the novel IST EoS and in Section 3 we present the mass–radius relation, including a discussion of constraints coming from nuclear and high-energy nuclear physics experiments. The paper ends with a summary in Section 4 . 2. Equation of State: Model Description The novel thermodynamically consistent EoS is based on the virial expansion applied for the multicomponent mixtures with hard core repulsion (Sagun et al. 2014 ). In particular, proper consideration of the volumes of particles enables us to explicitly account for the surface tension that is induced by the interaction between constituents. In this formalism the IST EoS has the form of a system with two coupled equations, one for pressure p and another for the IST coefficient σ defined as follows,andwhere T , m i , , and R i are temperature, mass, chemical potential, and the hard core radius of the i -sort of particles. The eigenvolumes and surfaces are equal to and . The summations in Equations ( 1 ) and ( 2 ) are made over all types of particles and their antiparticles, with a corresponding partial pressure of point-like particles of type i . Here, denotes the shifted chemical potential due to the presence of the hard core repulsion. The dimensionless parameter α in Equation ( 2 ) was introduced due to the freedom of the Van der Waals extrapolation to high densities (Sagun et al. 2014 ) and accounts for the higher-order virial coefficients. As was shown in Sagun et al. ( 2014 ) to reproduce the correct phase-diagram properties of nuclear matter, such a parameter should obey the inequality . According to the conditions of wide causality range and compressibility factor, the value of the parameter α in the Statistical Multifragmentation Model was found to be equal to 1.25 (Sagun et al. 2014 ) . Further studies revealed the value α = 1.245 (Sagun et al. 2017b ) is best for reproducing the fourth and third virial coefficients. Another physical meaning of α is as a switcher between the excluded volume and the proper volume regimes (for details, see Sagun et al. 2017a ). As the value α = 1.245 was obtained for the Boltzmann statistics (Sagun et al. 2017a ) and could be different at zero-temperature, when quantum effects are significant, the baryon radius and α parameter are chosen to be free parameters in the model. On the other hand, when fitting the mass–radius curve to existing