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We calculate the speed of sound $c_s$ in an ideal gas of resonances whose mass spectrum is assumed to have the Hagedorn form $rho(m) sim m^{-a}exp{bm}$, which leads to singular behavior at the critical temperature $T_c = 1/b$. With $a = 4$ the pressure and the energy density remain finite at $T_c$, while the specific heat diverges there. As a function of the temperature the corresponding speed of sound initially increases similarly to that of an ideal pion gas until near $T_c$ where the resonance effects dominate causing $c_s$ to vanish as $(T_c - T)^{1/4}$. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around $T_c$, the actual critical behavior in these models is no longer present.
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The speed of sound ($c_s$) is studied to understand the hydrodynamical evolution of the matter created in heavy-ion collisions. The quark-gluon plasma (QGP) formed in heavy-ion collisions evolves from an initial QGP to the hadronic phase via a possible mixed phase. Due to the system expansion in a first order phase transition scenario, the speed of sound reduces to zero as the specific heat diverges. We study the speed of sound for systems, which deviate from a thermalized Boltzmann distribution using non-extensive Tsallis statistics. In the present work, we calculate the speed of sound as a function of temperature for different $q$-values for a hadron resonance gas. We observe a similar mass cut-off behaviour in non-extensive case for $c^{2}_s$ by including heavier particles, as is observed in the case of a hadron resonance gas following equilibrium statistics. Also, we explicitly present that the temperature where the mass cut-off starts, varies with the $q$-parameter which hints at a relation between the degree of non-equilibrium and the limiting temperature of the system. It is shown that for values of $q$ above approximately 1.13 all criticality disappear in the speed of sound, i.e. the decrease in the value of the speed of sound, observed at lower values of $q$, disappears completely.
We argue that recent high energy CERN LHC experiments on transverse momenta distributions of produced particles provide us new, so far unnoticed and not fully appreciated, information on the underlying production processes. To this end we concentrate on the small (but persistent) log-periodic oscillations decorating the observed $p_T$ spectra and visible in the measured ratios $R = sigma_{data}left( p_Tright)/sigma_{fit}left( p_Tright)$. Because such spectra are described by quasi-power-like formulas characterised by two parameters: the power index $n$ and scale parameter $T$ (usually identified with temperature $T$), the observed log-periodic behaviour of the ratios $R$ can originate either from suitable modifications of $n$ or $T$ (or both, but such a possibility is not discussed). In the first case $n$ becomes a complex number and this can be related to scale invariance in the system, in the second the scale parameter $T$ exhibits itself log-periodic oscillations which can be interpreted as the presence of some kind of sound waves forming in the collision system during the collision process, the wave number of which has a so-called self similar solution of the second kind. Because the first case was already widely discussed we concentrate on the second one and on its possible experimental consequences.
The thermodynamical quantities and response functions are useful to describe the particle production in heavy-ion collisions as they reveal crucial information about the produced system. While the study of isothermal compressibility provides inference about the viscosity of the medium, the speed of sound helps in understanding the equation of state. With an aim towards understanding the system produced in the heavy-ion collision, we have made an attempt to study isothermal compressibility and speed of sound as a function of charged particle multiplicity in heavy-ion collisions at $sqrt{s_{NN}}$ = $2.76$ TeV, $5.02$ TeV, and $5.44$ TeV using Pearson formalism.
We consider planar hairy black holes in five dimensions with a real scalar field in the Breitenlohner-Freedman window and show that is possible to derive a universal formula for the holographic speed of sound for any mixed boundary conditions of the scalar field. As an example, we locally construct the most general class of planar black holes coupled to a single scalar field in the consistent truncation of type IIB supergravity that preserves the $SO(3)times SO(3)$ R-symmetry group of the gauge theory. We obtain the speed of sound for different values of the vacuum expectation value of a single trace operator when a double trace deformation is induced in the dual gauge theory. In this particular family of solutions, we find that the speed of sound exceeds the conformal value. Finally, we generalize the formula of the speed of sound to arbitrary dimensional scalar-metric theories whose parameters lie within the Breitenlohner-Freedman window.
The existence of massive compact stars $(Mgtrsim 2.1 M_{odot})$ implies that the conformal limit of the speed of sound $c_s^2=1/3$ is violated if those stars have a crust of ordinary nuclear matter. Here we show that, if the most massive objects are strange quark stars, i.e. stars entirely composed of quarks, the conformal limit can be respected while observational limits on those objects are also satisfied. By using astrophysical data associated with those massive stars, derived from electromagnetic and gravitational wave signals, we show, within a Bayesian analysis framework and by adopting a constant speed of sound equation of state, that the posterior distribution of $c_s^2$ is peaked around 0.3, and the maximum mass of the most probable equation of state is $sim 2.13 M_{odot}$. We discuss which new data would require a violation of the conformal limit even when considering strange quark stars, in particular we analyze the possibility that the maximum mass of compact stars is larger than $2.5M_{odot}$, as it would be if the secondary component of GW190814 is a compact star and not a black hole. Finally, we discuss how the new data for PSR J0740+6620 obtained by the NICER collaboration compare with our analysis (not based on them) and with other possible interpretations.
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