|The energy equation building blocks that Richard Feynman played with as a child, on the cover of the 2010 book Energy, the Subtle Concept, by nuclear physicist Jennifer Coopersmith. |
The focused study of energy is called energetics, which has limited application, or thermodynamics, when, in addition to energy, entropy is taken into account, which has universal application.
There does not seem to be a unified and exact etymology to the word "energy", aside from the general agreement that the term originated in ancient Greek science, particularly in the works of Heraclitus and Aristotle, in its primordial concept wording and description.
Beyond this, there is the famous Thomas Young 1802 equation definition of energy described as kinetic energy, as we now understand kinetic energy; there is the super-famous Rudolf Clausius 1850-1875 thermodynamic definition of energy as internal energy or energy of the body as a function of various differential quantities or state variables, at which point "energy" became the universal entity; and lastly there is the superstar status of energy as being equivalent to mass as formulated by Albert Einstein in 1905.
Heraclitus: The the earliest etymological reference to the use of the term “energy” is found in the circa 500BC writings of Greek philosopher Heraclitus (c.535-450BC), the so-called “flux and fire philosopher”, who used the term en-ergon, meaning "the source of activity". Heraclitus, in his book about nature, according to American science writer Gerrit Feekes (1986), wrote: 
"En-ergon is the father of everything, king of all things and, out of it, all forms of contrast originate. Since ‘en-ergon’ is common to everything, it is vital for life itself.”
Likewise, Canadian sociophysicist Paris Arnopoulos (1993) attributes the coining of energy to Heraclitus, as follows: 
“The term energia was first used by Heraclitus to connote fire as the primary source of action. Heraclitus, in his Physics, considered Energon the father of everything and the originator of all life on Gaia.”
Arnopoulos also states that Empedocles was the first to distinguish between "matter", which he conceptualized as earth, water and air, and "energy", which he conceptualized as fire or heat.
Aristotle: The most widely cited etymological origin of "energy", however, is that it derives from the works of Greek philosopher Aristotle particularly his circa 350 BC Metaphysics in which he used the term Greek term ἐνέργεια (taken over into Latin as energia) with the meaning, “according to scholars”, as discussed in American physicist Robert Lindsay’s respected 1975 book Energy: Historical Development of the Concept, of the “realized state of potentialities”, presumably having to do with that which has the ability to bring about something else. 
Likewise, American physical economics historian Philip Mirowski, who spent over six years doing research in on the used of physicist notion of energy and the conservation of energy being employed in economic theory, cites Lindsay, and explains that Aristotle used the word in several senses: in his Ethics, in the sense of “activity” as opposed to mere disposition; in his Rhetoric, for a vigorous style. Aristotle also employs it to distinguish activity from potentiality, and to imply the ceaseless transformation of the potential into the actual. 
Recent etymology dictionaries, similarly, give an Aristotle etymological origin to the “energy”, citing his circa 350 Metaphysics, describing the term enérgeia to mean act or ‘activity’, ‘actuality’, or in a literal sense ‘(a state of) functioning’; but itself deriving from, what seems to be the earlier Heraclitus use of the Greek term "ergon" or energos meaning "active, working," from en- "at" + ergon "work". 
In sum, Aristotle used the term enérgeia to clarify, in one sense, the definition of “being” as potency (dýnamis) and act (enérgeia).
The modern spelling of the term “energy” is said to have came into use in 1599. 
Papin: In 1690, French physician and physicist Denis Papin, in his famed memoir “A New Way to Obtain Very Great Motive Powers at Small Cost”, used the term energy in a somewhat modern sense. Specifically, according to Papin, the forceful downward movement of a piston, by the pressure of the atmosphere, in an evacuate cylinder, having been evacuated by the quick condensation of steam, which thus created a partial vacuum, was said to be proportional to an amount of energy. In his own words: 
“[The quick condensation of steam] [in the vacuum engine] [gives the] intended movement; which is of an energy great in proportion to the size of the tube.”
In the 1728 Cyclopedia - or Universal Dictionary of Arts and Sciences, one of the first general encyclopedias to be produced in English, energy is defined as “an uncommon force, or strength, in a discourse, a sentence, or a word.”  In 1775, energy was defined as “there is in a body in movement an effort of energy which is not at all in a body at rest”. 
Young: The modernly defined usage of the term energy, as pointed out by James Maxwell (among others), was made by English physicist and physician Thomas Young. In 1802, Young began to write a series of lectures on natural philosophy for the Royal Society, by the request of American-born English physicist Benjamin Thomson, which were finished in 1807 and amounted essentially to a treatise on everything that was known in modern science in that day. In his lecture "On Confined Motion", Young states:
“Since the height, to which a body will rise perpendicularly, is as the square of its velocity, it will preserve a tendency to rise to a height which is as the square of its velocity, whatever may be the path into which it is directed, provided that it meets which no abrupt angle. The same idea is somewhat more concisely expressed by the term energy, which indicates the tendency of a body to ascend or to penetrate to a certain distance, in opposition to a retarding force.”
In his lecture “On Collision”, the most cited of his definitions of energy, Young states:
“The term energy may be applied, with great propriety, to the product of mass or weight of a body, into the square of the number expressing its velocity. Thus, if the weight of one ounce moves with a velocity of a foot in a second, we call its energy 1; if a second body of two ounces has a velocity of three feet in a second, its energy will be twice the square of three, or 18.”
This usage, according to Ingo Muller, supposedly, is based on the Greek word ένεργεια meaning efficacy or effective force, as an abbreviation for the sum of kinetic energy and gravitational potential energy of a mass and the elastic energy of a spring to which the mass may be attached.  In this sense, Young defined energy as:
To clarify that Young was the first to have mathematically coined the term "energy", years later Scottish mathematical physicist William Thomson stated before an audience, for instance, that “the very name energy, though first used in its present sense by Thomas Young about the beginning of this century, has only come into use practically after the doctrine which defines it had ... been raised from mere formula of mathematical dynamics to the position it now holds of a principle pervading all nature and guiding the investigator in the field of science.” 
Lagrange: Four years later, supposedly in 1811, in partial correction to Young’s expression, Italian mathematician Joseph Lagrange used calculus to show that a factor of two is involved in the relationship “potential” (potential energy) and “vis viva” (kinetic energy), and thereby defined energy as: 
To note, the exact publication and derivation of this half factor still needs to be tracked down; although it seems to have its origin in Lagrange's 1788 Analytical Mechanics, of which the second edition was published in 1811-1815.
To note, according to a second reference (Max Jammer), it was French physicist Gustave Coriolis who in 1829 introduced the factor ½ in Leibniz’s vis viva for the sake of mathematical convenience. 
To note, according to a third reference (Philip Mirowski), it was Swiss mathematician Leonhard Euler who introduced the ½ factor in 1752.  This latter citation, which is based on American physicist Robert Lindsay's 1976 Energy: Historical Development of the Concept, however, may be a misinterpretation.
Clausius: In 1864, German physicist Rudolf Clausius, in his "On Terminology" section, Appendix A to his Sixth Memoir, adopted the term "energy", semi-based on William Thomson's earlier usage, for his new thermodynamic quantity U, otherwise known as "internal energy" in modern parlance, as follows: 
“Of the expressions mentioned above—namely: ‘the mechanical energy of a body in a given state’ (Thomson), ‘wirkungsfunction’ (Kirchhoff), and ‘interior heat of body’ (Zeuner)—the term energy employed by Thomson appears to me to be very appropriate; it has in its favor, too, the circumstance that it corresponds to the proposition of Rankine to include under the common name energy, both heat and everything that heat can replace. I have no hesitation, therefore, in adopting, for the quantity U, the expression energy of the body.”
Clausius, in short, building on the earlier work of Irish mathematician William Hamilton (1833), who showed that for a system of particles the sum of the kinetic energy and potential energy in the system can be represented by a set of differential equations known as the Hamilton equations for that system, showed that the energy U of a system, equates to the sum of the “vis viva” (kinetic energy), symbol T, and the “ergal” (potential energy), symbol J, of the three-dimensional movements of the particles of the system, such that:
and the "energy remains constant during the motion" (conservation of energy). 
Planck: The best modern-day general definition of "energy" was given by German physicist Max Planck, the noted PhD student of the work of Clausius, who gave the following (Clausius-based) definition of energy, supposedly, in argumentative correspondence with German physical chemist Wilhelm Ostwald in the period of the great "energetics debate" (c.1895): 
“[A]n energy is a quantity which depends only on the instantaneous state of the system, not on the manner in which the system reached this state or on the manner in which it later changes its state. The whole importance of the concept of energy rests on this property; without it the principle of the conservation of energy would be illusory.”
The reason this definition is the most cogent of all energy definitions is that once the appropriate reference frame is chosen, the "states" of all of the various energies of bodies or systems in the universe can be measured, quantified, and tabulated in thermodynamic tables, such as are found in free energy tables.
Einstein: In 1905, with respect to the development of "relativistic thermodynamics", German-born American physicist Albert Einstein showed that energy is proportional, according to the speed of light squared, to matter, in what has come to be called in word format as "mass-energy equivalence" relation or in equation format famously as E = mc².  Specifically, in his paper "Does the inertia of a body depend upon its energy-content?", Einstein proposed that the equivalence of mass and energy is a general principle, which is a consequence of the symmetries of space and time: 
This has since come to be known as the most famous equation in all of science.
Into the late 20th century, in the perspective of particle physics, energy, in contrast to matter, began to be defined structurally as bosons or Gauge bosons.
See also: human energy, social energyIn human chemistry, energy can be released or absorbed through the transformations of human chemical bonds.  The mathematical connection between the bulk measurements or "state" measurements of energies of human thermodynamic systems, such as a country, to the individual working energy actions of people (human molecules), as mediated through working human bonds, is new area of research. 
● Potential energy
● Kinetic energy
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(b) Mirowski, Philip. (1989). More Heat than Light: Economics as Social Physics, Physics as Nature’s Economics (pg. 22). Cambridge University Press.
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● Energy – Visuwords.com.
● Energy – Wikipedia.