Entropy waves are an important source of indirect combustion noise and potentially contribute to the generation of thermoacoustic instabilities in gas-turbine combustors. Entropy fluctuations generated by unsteady combustion are known to disperse and diffuse as they convect toward the combustor exit. In this work, the propagation of entropy waves is investigated by means of experiments in a newly developed entropy rig and numerical simulations based on the large-eddy simulation approach. Both experimental and numerical results demonstrate that the amplitude of entropy fluctuations decays as a function of wave parameters and propagation distance, and it scales well with a local Helmholtz number $He$. A new theoretical model for the computation of the entropy transfer function suitable for inclusion in low-order models for combustion instabilities is proposed. Assessment against numerical and experimental results shows the capability of the model to give a proper representation of the decay of entropy waves in terms of both magnitude and phase of the entropy transfer function. Furthermore, by comparison with the large-eddy simulation results, it is shown that, at low Helmholtz numbers, the contribution of the differential convection to the decay of entropy waves is dominant; whereas for high values of the Helmholtz number, the turbulent mixing and diffusion also become important.