As far as I know ordinary waves do not change the entropy of the gas, whereas shock waves do.
Could someone please explain the reason behind this difference?
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Your question relates to what happens to the entropy during the propagation of a wave.
Any wave that maintains its form, e.g. a soliton, will require no more and no less information to characterise its state as it propagates. The only circumstance in which more or less information is required is when the wave form changes over time. In the case of shock waves, their form dissipates rapidly, and thus the information required to describe it also changes (the entropy increases).
In the case of shock waves, the gas is subjected to a very rapid deformation in which viscous dissipation of mechanical energy to internal energy is occurring. The rate of entropy generation can be shown to be proportional to the rate of viscous dissipation divided by the absolute temperature. So the entropy of the gas increases. For more details on this, see Transport Phenomena by Bird, Stewart, and Lightfoot.