Physical power and social power are much the same thing because they both derive from energy. That’s the rough thesis of a recent article by Edmund Russell and a rugby team of co-authors (The Nature of Power: Synthesizing the History of Technology and Environmental History). To show it’s not just a cheap academic party trick, they then use it to rewrite the history of the Industrial Revolution in terms of energy flows. 

The social power of mill owners and the physical power of the explosion flowed from a common root: the ability of mill owners to concentrate wheat in one building, which enhanced their control over a high value–added link in the product chain and increased their social power. If all of that wheat had been ground in hand-mills scattered among thousands of homes, the Minneapolis mill owners would have had little power, and any individual explosion would have been relatively weak. Indeed, Karl Marx argued that forcing people to abandon hand-mills and bring their grain to centralized water-mills was one way in which capitalists gained power in Europe.

The basic insight extends a house theme of Technology and Culture, that technological networks require or include institutional social networks. Railways imply drivers, engineers and conductors. (Tootle tells all the young engines to stay on the rails, no matter what.)

So we’re certainly several steps beyond claiming string theory can derive the Peloponnesian War (given a perfectly spherical map of Greece and an unlimited supply of starving grad students). Energy centric analysis can uncover neglected historic and social connections, and is actually pretty cool. The authors go quite a bit further than that, though:

Our thesis is that all power, social as well as physical, derives from energy.

This is plausible enough but seems a little undercooked. The authors are careful to avoid a claim of equivalence for the two types of power, but the weaker claim of derivation still seems to need exploring. In the physical definition, power is a mathematical derivative of energy with respect to time. The nature of the social derivation is left undefined. I am showing my physical science bias here, but without a more precise definition this claim just seems to trade on a metaphorical connections between different meanings of “derive”.

Again, even if this is simple overstretch, energy-centric history is still rather neat. In a spirit of constructive speculation, though, I can think of two ways social power might be a derivative of energy in a quantitative sense.

One option is simple equivalence, the rate if energy delivered over time. It should be quite possible to, say, describe the military power deployed in the hundred hours of the Operation Desert Storm ground campaign in terawatts. This would be an involved accounting exercise based on inputs of fuel, food, ammunition fired, amortized energy capital costs, and so on. Presumably some high level estimate could be made after a few days or weeks effort. Such a stat might be of use to economic or military historians, though the deployment of military energy is notoriously prone to inefficiency and involves specifics of formation and timing. E.g., consider the energy budgets at work in the Indochina War.

Political power as a scalar doesn’t fit well with the intuition that it is something attributable and directed. People and organizations have power due to their relationship to others. This suggests a more radical, speculative definition: social power is energy derived with respect to paths on a social network. This has intuitive appeal, but for now I am throwing it out there without detailed exploration or justification.

Contrariwise, maybe the social network can be considered just another network for energy distribution. We have electricity and food distribution networks after all. Perhaps adding above them is an unnecessary metaphysical duality. The US president can order aircraft carriers into motion, they require lots of petrol, he is therefore powerful. Financiers have money which can be turned into electricity – potential energy.

Either way it seems right that social power should be intertwined with control of flow. 

Even the organization within which, as was previously supposed, the individuals treat each other as equal—it takes place in every healthy aristocracy—must itself, if it be a living and not a dying organization, do all that towards other bodies, which the individuals within it refrain from doing to each other it will have to be the incarnated Will to Power, it will endeavour to grow, to gain ground, attract to itself and acquire ascendancy—not owing to any morality or immorality, but because it LIVES, and because life IS precisely Will to Power
— Nietzsche, Beyond Good And Evil, Zimmern trans.