In thermodynamics, an adiabatic process is one that occurs without transfer of heat or mass of substances between a thermodynamic system and its surroundings. In an adiabatic process, energy is transferred to the surroundings only as work.
If we’re talking about photons, then yes, you could (in principle) have some sort of phenomenon which redshifted them while still being frame-invariant (though no good evidence has ever been found for this). But for massive particles, it wouldn’t work.