→ Empire, extraterritoriality, sovereignty, state, territory
The notion is polysemic, which requires the elimination of a series of meanings not relevant in this case, although the semantic relationships between the various uses of the term shed some light on the meaning used in international relations (IR).
The various means, rights and resources that enable an actor to act, influence or decide are central to the basic meaning of the term insofar as it refers to an active reality. But it also conceals, in a logical and philosophical sense, potential or virtual dimensions. This can be seen in the distinction that applies to empires, states or other political actors in the sense that nominal power (military means, territorial extension, moral and political authority, etc.) does not necessarily translate into effective power, as demonstrated by the "great powers" of the 20th century such as the United States in Vietnam or the USSR in Afghanistan, politically defeated by non-state actors and forced into a retreat.
The term power also has a variable extension that contrasts with the term "power" or "powers" (which are not exact synonyms, as Pierre Verluise  says), which designate in a more static and formal way the legally or empirically defined capacity to have means or rights that can produce an effect, even if the term also has, in other contexts, the meaning of "potentiality" conferred by power (assimilation, purchase, speech, music, numbers, extrasensory or divinatory power in the sense of faculty, etc.). The "power" of a State will therefore appear vague with regard to the "separation of powers" required by the legal definition of the corresponding institutions and their interrelationships, as well as the "powers" of international organizations defined by the treaties. This distinction is particularly explicit in French, whereas English remains implicit when it refers to these two realities of the same term, whatever the gender: power(s) (superpower, great powers) and power(s) (soft power, separation of powers in the Constitution, powers of arrest and interrogation, etc.).
On the other hand, the notion of power, unlike that of power, is tense by a vector with a unidirectional direction, because if we can speak of great power, hyperpower, superpower, average power, (re)emerging or declining power, new or old power, we will hardly speak of "small power". It was this unidirectionality that prompted Hubert Védrine in 1998 to speak of "hyperpower" about the United States after the collapse of the USSR, not only to evoke the birth of a form of unipolarity, but also to designate both hard power and soft power (i.e. powers) in American America. The gradation of the sense of power is expressed at different levels: intensive (from medium to hyper), geographical (from regional to global), temporal (from emergence to death, empires in particular).
The variable expression or constraint of power has led some researchers to point out the importance of the concept of "powerlessness" in situations where power is effectively blocked or even defeated by opposing forces that are in a state of inferiority in terms of material resources, but superior in the social or ideological field (de Montbrial 2013, Badie 2005, 2018). Impotence will therefore be considered as a structuring factor of IR, in the same way as the first, state actors, retained by IR theorists in varying proportions. The resilience of the Islamic state today is a singular example, weakened, admittedly, by the unwelcome search for a "state" identity (Islamic state in Iraq and in the Syrian Rising Cham) for a time, but which remains rooted in certain segments of the populations of Muslim culture. We can measure here the struggle that is emerging between power and power, the state entity being confronted with religious power in the opposite direction to what the West is experiencing, because, if the state structure is not condemned, the ambition of the Islamic state to resurrect the caliphate has its roots in the history of Islam, whose universalist ideology has always been oriented towards its imposition on all humanity, it being understood, as stated in the Koran and the comments of Muslim lawyers, that any state entity or political structure must remain subordinate to the power, and the word is well used here, of religion (we recall Michel de Certeau's original study in La Possession de Loudun, published in 1973, which relates the clash in Loudun, in 1634, of religious, political and scientific powers).
It should be noted in passing, with regard to the latter example, that the concept of the State, associated with that of power, is tainted by its own ambiguity. While it theoretically designates a well-defined political entity from a Hobbesian perspective as the actor who enjoys a monopoly of legitimate physical violence on a territory and the powers that come under it and, as such, remains at the foundation of international order (or disorder), its application in the political field is particularly elastic, since the very meaning of the term "State" covers contemporary States as well as empires or certain traditional structures in its uses. Historians and anthropologists describe the Chinese Empire as a state, as much as any traditional African policy with a formal political structure (Balandier 1967), or the confederations of Mongolian tribes at the end of the 12th century, which led to the Mongolian empire of the 13th century (Testot 2014-2015). This focus stems from a 19th century historiography concerned with exalting the national state or belittling previous periods to highlight the merits of state construction and, hence, of the nation state, whose contemporary era is undergoing a new glorification.
This leads to a second remark on the permanence of the State and the paradigm it bases, or conversely its impermanence, that it finds itself confronted with the legacy of history, weakened by the "return" of empires (Minin 2013, Grosser 2013) or by the power (in the first sense) of transnational agents - religious or, today, economic and financial (Hoeber Rudolph 1997). Recent history has thus seen economic thinking impose itself on all political, philosophical and ethical conceptions with Adam Smith (professor of moral philosophy and not economics), Karl Marx, Jean Charles de Sismondi (economist and philosopher), John Maynard Keynes (author of philosophical writings), Thomas Malthus, Alfred Marshall and John Stuart Mill, until the patent failure of the economic paradigm reflected in the 2007 financial crisis. In general, historians relativize the centrality of the state in history and describe the nation-state, or even the contemporary state, as a "blip" or "parenthesis" in political history (Burbank and Cooper 2010). Throughout history, peoples have lived within political entities that did not claim to represent a single or homogeneous people. Before the rise of Western-style states, power passed through empires, from antiquity to colonial empires. Similarly, the era of the superpowers after the Second World War saw the USSR and the Eastern bloc confront each other in a "cold war", on the one hand, of which Cuba was an outgrowth, and the United States and the Western bloc on the other, with the Berlin Wall acting as a symbol as a geopolitical border, from its birth to its fall.
Finally, associating state power with the notion of border presents another difficulty. The notion of border as a defining element of the classical state is as much a construct as the state and the nation state. Political anthropology has indeed been able to describe, within very similar societies, stateless communities alongside communities of the same nature with a state structure (Balandier 1967, 1985). Below the state stratum, the notion of border fluctuates according to history and represents multiple realities that do not stop at politics, but call upon cultural and psychological ingredients, from the surface to the great depths. It would be difficult to attribute a border to the "maritime power" that England was, to Napoleonic France as a "land power", to the "technological power" that the United States represents and that aims to become China, or to the cybernetic power that these two "States" are aiming for in the 21st century. Similarly, cultural or linguistic mapping reveals a complex and shifting entanglement of boundaries, limits, margins and other boundaries of the corresponding territories, which are not the case for Jewish, Roma (the largest minority in Europe) and other diasporas.
To return to a more formal notion of power and taking into account computer resources, Pierre Verluise and his colleagues (2015) classify powers into four categories: cyberpowers (United States and China), cyber-dragons (Israel, Taiwan, Singapore and South Korea), cyberspace deserters (Europe and Japan), a secondary actor (India) and an almost absent one (Russia). The intelligence tools used as parameters are submarine cables, NSA access points to cable landing stations, and an American submarine model capable of making secret connections on submerged cables.
Another defining characteristic of power is extraterritoriality, such as the effects of US legislation on international trade, the sanctions it imposed against Cuba in the 1990s or against Iran today. Certainly, the rape of the sovereignty of a weak state by a powerful state is a general rule in the history of inter-state relations, which is vividly illustrated by colonialist enterprises and the expansion of empires throughout history. However, it is facilitated by the tacit or negotiated renunciation of certain States, which, like the EU Member States, are not economically weak, to exercise their traditional prerogatives and grant the hyperpower or superpower fields of extraterritoriality that allow it to freely exercise the defence of its interests. The criteria applied are not very different from those of empires, ideological movements or religions with a universalist aim, whose territorial limits are never fixed. It is the same renunciation, if not complicity, that has allowed non-state actors such as multinational companies, better known as transnational corporations, to impose their criteria on powers, small and large. The recent case of Monsanto is significant in this respect, which imposes its criteria on the agricultural world as a whole and whose legal position directly competes with state or supra-state (EU) powers (Shiller and Shiller 2011). But here, as in other areas, Christophe Bouillaud (2017) notes that the issue would not so much be the powerlessness of States as their renunciation of the action of transnational groups, networks and other actors, but also of the interests of local or national minorities, the consequence of which is to exclude a variable part of their own citizens (women, disadvantaged classes, cultural minorities) and, in so doing, to reduce their rights even in their democratic expression.