why do hot composting and tilling burn more organic matter?

I've read many times that making a hot compost pill or tilling will increase the rate that you burn through  the organic matter in the compost pile or soil. As I understand it, this is because the heat in a compost pile or the air added when tilling encourages rapid growth in soil organism populations which break down the organic matter faster. However, I don't understand where the losses come from. The organic matter is being converted to micro and macro soil organisms, which is just a different kind of organic matter. Is it correct that one loss comes from the respiration of the soil organisms, which will result in loosing a certain percentage of the carbon in the original organic matter? What other losses (inefficiencies) result from this process?

i think we have to distinguish tilling from composting.
(i am just gonna sum up what i know of it, i might be repeating stuff you allready know)

As i understand it, in both cases the added oxigen stimulates mirco organisms.

In the compost however it just speeds up the processes of breaking down organic matter in soil. The new form being something that is added to the soil and partly available for plants to take up with roots, partly further taken down by topsoil organisms.

When tilling soil we also stimulate soil organisms. But in contrary to a compostheap where undecayed materials (carbons and nitrogens in the right ratio, if the heap is built right) are readily available to be used, and converted into nutricients, when tilling soil we can stimulate the soil organisms in a way that they start using already available nitrogen in the soil for its processes. This N is allready converted and stored in the soil that, when untilled, realeases it slowly to roots.

So both tilling a compost heap and tilling soil increases the activity of most mirco-organisms (i assume mainly bacteria) but the effects, are different and in one case positive and the other negative.

By the way, as far as i know a hot compost is not necessarily tilled. A hot compost is built by starting with at least 1 m2 of compost and building it up in the right ratio of dry and wet, brown and green (carbon.nitrogen) materials. The compost than heats up to temperatures above 60celcius (killing lots of seeds and pathogens, and also decomposes very quickly.

A cold compost, which isnt cold at all, is the type that is more often tilled to increase the decay. But this is all temperate (dutch) climate info, dunno how it could be different elsewhere...

In a word, Metabolism.

Only a small percentage of complex carbon is turned into flesh.  Roughly half gets passed through as feces for the next user.. the other half gets deconstructed inside cells for the energy embedded in the molecular bonds between the carbon molecules (captured sunlight back on the photosynthesis side of the cycle)... the end output of metabolism is carbon dioxide gas which returns to the atmosphere... which is why Nitrogen and Carbon are sometimes called the 'gaseous nutrients'.

I have not seen the science to back up the assertion that surface placement of organic waste results in more stable humus in the soil compared to other pathways of organic matter recycling.  Surface litter also 'volatilizes' and turns into CO2 with no benefit.  Optimal composting would likely result in a higher percentage of carbon being converted to feces and flesh than an equivalent pile left on the surface (at a cost to you in labor).  Then again there are other benefits to a litter layer.

The point about proportions of carbon which go toward metabolism versus tissue and waste is the heart of the matter. Most especially, it's important to see how stable the waste carbon is: humus comes in many different flavors, so to speak.

I think the individual soil and/or compost ecosystem has to be accounted for: the greatest humus creation might take different methods in different climates.