At the HVAC Hub discord server, I asked this question, and they saying that this is true, but I don't understand how.
I only know that in on/off A/C the compressors always works at 100% speed and turned on/off, and in inverter A/C, the compressor changes its speed.

Of course inverter AC is more efficient than fixed speed compressor units.
Once the room is cooled to the desired temperature the compressor just runs slowly to maintain the temperature instead of running at full speed on and off every few minutes.
This really is pretty basic stuff and should be obvious.
Think of driving a car: you don't keep flooring the accelerator and then suddenly let right off only to repeat this sequence a few seconds later to maintain roughly the same speed. If you imagine the poor fuel comsumption this would give then this corresponds to the similar reduced efficiency of fixed speed AC units in most situations.

This really is pretty basic stuff and should be obvious

And also is wrong

Once steady state is achieved (the condition in which the inverter unit winds down), the air conditioning unit output, averaged over time, equals the heat loss (or gain, if we are in the summer) through the room walls. This heat loss depends linearly and exclusively on the temperature difference between the room (chosen by the user) and outside (determined by the weather), and insulation resistance of the room walls

The air conditioning unit has no effect on the heat loss. In case of an on/off switching unit, the hysteresis beween the on and off temperatures is way less than the temperature difference between indoors and outdoors, so in average it still has no effect on the heat loss

The air conditioning unit then must pump the same quantity of heat/time unit in or out to maintain the temperature difference constant. Heat is energy, heat per time unit is power

Consider 2 compressors with identical COP but different power. One is of the exact power required to counter the heat loss, and the other is 2x the power. The 1x one will work continuously, the 2x one will work with 50% duty cycle. Twice the power for half the time is the exact same energy

So no, thermodynamics absolutely don't confirm this basic stuff



Now let's look at the electrics

The on/off unit has a simple induction motor. There is no principal limit on the efficiency of such motor. Having to work only in a single set of conditions (same power, same refrigerant pressures, ...) it seems obvious to optimize this motor for working at this exact set of conditions

Limiting the efficiency of such motor (and consequently the COP of the unit) is only cost - If using a bigger motor with room for thicker winding, Using lowloss steel in the laminations, etc. The motor can be made to any desired efficiency

The inverter unit has a similar induction motor. It is basically a plain 3 phase motor, though most of them are not for 50/60 Hz but for somewhat higher frequency

Higher frequency allows for smaller cores and less turns in each winding (which means thicker wire can be used in the same motor size), same as in lighting ballasts. However, there are few parts that can pull efficiency down as well :

 - The stator is still made of laminations, which dont behave well above few 100s Hz. (Eddy currents, hysteresis losses, increasing loss in general)

 - The motor must work efficiently in a broad range of speeds and pressures. Is it optimised for the exact ones at which it'll run in your case ?

 - The inverter itself also got losses

Considering that 50/60Hz induction motor efficiency is typically 85%..90%, this gives a clue of the theoretical upper limit of energy you might save if the inveter and inverter powered motor would be 100% efficient

In reality, the motor is probably closer to the same 85..90% as the other motor, and the inverter has a few % left behind as well



At this point, it is no longer about any significant energy savings, but blatant shoving of advanced technology where it is not needed