Bureaucracies and administrative hierarchies generate (at least) two types of entropy: useless and useful. Useless entropy is that which is the inevitable cost and loss of all ordered systems: the degeneration into thermodynamic equilibrium of formless chaos and random noise, represented by waste heat, noise, literal garbage and human waste or unrecoverable cost and the unsurprising discarded value and unrecoverable cost of many of those inefficiences borne of bureaucratic or hierarchical and administrative inertia.
Useful entropy is that which would otherwise rapidly devolve into useless entropy but for which the various internal logical and symbolic or representational practices and methods of organisational systems have developed strategies and formal processes to capture and recycle the potential energy or useful information encoded in that organisational waste product. The fact that it is even plausibly “useful” already indicates that it is not genuinely entropic or completely random but that it represents some kind of potentially recyclable internal organisational value.
Organisations tend to optimise their energy and information flows and patterned processes in ways which minimise the generation of useless entropy while recycling useful entropy back into the rationale and logic of the organisational system. Under this analysis, we are able to intuit that (a sub-set of) organisational inefficiencies are also methods of preempting the inevitable generation of useless entropy by unconsciously, unintentionally or otherwise unwittingly generating useful forms of inertia, confusion and double-handling or duplication so as to recycle what may otherwise be lost to the degenerative vacuum of the 2nd Law of Thermodynamics.
Granted, there could be an unjustifiable leap of faith here in attributing the generation of organisational inefficiencies to the same thermodynamic principles that degenerate ordered systems into randomness and chaos but that is not, strictly, what I am intending to say. The meaning intended here is more that emergent complexity in organisational (as much as in any other natural) systems possesses various internal biases and symmetries which predispose those systems to seeking out the most effective strategies and vectors through which to self-propagate themselves. This is true of both living and (many) non-living dynamical systems. Entropy and waste is inevitable but emergent and adaptive methods or strategies of usefully recycling energy and information in self-supporting ways is a method to minimise loss and unrecouped cost. The implication here is that this is not necessarily an organisational principle functioning at the level of conscious awareness, and consequently that seeking to intentionally harness such dynamical organisational symmetries could prove to be a non-trivially subtle or difficult (but not necessarily impossible) heuristic task.
What organisational systems manage to achieve through all of this is to generate specific channels and instances of informational waste product which are then recyclable back into those same systems as useful complexity, the management and negotiation of which goes further to justifying the existence of those same organisations by giving them direction, purpose and continued work. This is why we might never expect anything beyond a certain (probably measurable) organisational efficiency dividend for any sufficiently complex bureaucracy or hierarchical administration.