Multiplicity Dependence of Shear Viscosity, Isothermal Compressibility and Speed of Sound in $pp$ collisions at $\sqrt{s}$ = 7 TeV

In order to understand the detailed dynamics of systems produced in $pp$ collisions, it is essential to know about the Equation of State (EoS) and various thermodynamic properties. In this work, we study the shear viscosity to entropy density ratio, isothermal compressibility and speed of sound of the system by considering a differential freeze-out scenario. We have used a thermodynamically consistent Tsallis non-extensive statistics to have a better explanation for the dynamics of $pp$ collision systems. While the shear viscosity to entropy density ratio provides information about the measure of fluidity of a system formed in high energy collisions, the isothermal compressibility gives a clear idea about the deviation of the system from a perfect fluid. The speed of sound in the system as a function of $\langle dN_{\rm ch}/dη\rangle$ gives us a vivid picture of the dynamics of the system. The results show quite an intuitive perspective on high multiplicity $pp$ collisions and give us a limit of $\langle dN_{\rm ch}/dη\rangle$ $\gtrsim$ (10 - 20), after which a change in the dynamics of the system may be observed.

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