What's wrong with the second law of thermo?
The amount of energy available to do work decreases over time. That more or less discusses what you were talking about. Are you trying to remember a specific phrase you once heard?
It looks to me that bigfield (and please correct me if I'm wrong, bigfield) is looking for a word to refer to the decay of things in general; IOW, he's not looking for a scientific word? Or are you, bigfield?
To quote, from your OP:
bigfield: ...Whenever systems are first made/set up, they often start off working well and then slowly settle into a state of decay.
e.g.
- an office space that starts off clean, tidy and organised but gradually becomes dusty, cluttered and disorganised.
- a car that starts off shiny and smooth-running slowly succumbs to weather and engine wear.
- a business or government department starts off energetic and productive but develops redundant bureaucracy, resource shortages or poor service delivery.
Atrophy also refers to the natural decay of muscles, skin, organs, etc. As we all know. So why the need for a scientific term when a "folksy" term works?
Sorry if I am overstanding [the opposite of understanding, right?].