Top: slow-mode temperature amplitude (left) and phase shift between temperature and velocity perturbations (right) given by Equations (16) and (17). The horizontal dashed line in the top right panel indicates the phase shift of π/2 in the ideal adiabatic regime. Bottom: entropy-mode temperature amplitude as a function of loop temperature and density given by Equation (18) (left) and that versus slow-mode temperature amplitude at fixed density ρ₀ = 5 × 10⁻¹² kg m⁻³ (right, in blue and red, respectively). The horizontal dashed line in the bottom right panel shows the adiabatic slow-mode temperature amplitude ﹩({A}_{u0}/{c}_{{\rm{s}}})\times (\gamma -1)\times \sin (2\pi {z}_{0}/{\lambda }_{0})\approx 0.054﹩ for A_u0/c_s = 0.1 and z₀ = 0.15λ₀. The dotted and solid black lines in the left panels indicate the entropy-to-slow damping time ratio τ_entropy/τ_slow = 0.3 and 0.1, respectively (see Figure 1). The red diamond shows the combination of ρ₀ = 5 × 10⁻¹² kg m⁻³ and T₀ = 6.3 MK used in our numerical analysis (Figures 2–4).