Lattice-data-driven specific heat and isentropic bulk modulus of SU(3) gluon matter at finite temperature

Abstract

Abstract We investigate the specific heat and isentropic bulk modulus of finite-temperature pure SU(3) gauge matter within a lattice-data-driven phenomenological framework. The equation of state is formulated in terms of a temperature-dependent effective gluon mass constrained by lattice QCD pressure data as input, allowing the pressure, trace anomaly, gluon number density, energy per thermally active gluonic mode, and derivative-sensitive response functions to be derived in a thermodynamically consistent manner. The resulting pressure and trace anomaly reproduce the characteristic lattice behavior across the deconfinement region, while the effective gluonic degrees of freedom increase rapidly above $$T_c$$ T c . The normalized specific heat $$C_V/T^3$$ C V / T 3 develops a pronounced enhancement in the vicinity of $$T_c$$ T c , reflecting the rapid temperature variation of the energy density across the deconfinement region. The isentropic bulk modulus $$K_S/T^4$$ K S / T 4 also rises sharply across the transition region, indicating a substantial stiffening of the equation of state. At high temperatures, both response functions gradually approach values close to their massless conformal Stefan–Boltzmann reference values, with $$\left( C_V/T^3\right) _\textrm{SB}=32\pi ^2/15\simeq 21.06$$ C V / T 3 SB = 32 π 2 / 15 ≃ 21.06 and $$\left( K_S/T^4\right) _\textrm{SB}=32\pi ^2/135\simeq 2.34$$ K S / T 4 SB = 32 π 2 / 135 ≃ 2.34 . These findings indicate that the specific heat and isentropic bulk modulus provide complementary constraints on the temperature evolution of nonconformal dynamics in pure SU(3) gauge matter.