The concept of energy change from one form to another, as a "driver" for natural processes, is useful in explaining many phenomena. In particular, since energy cannot be created or destroyed, the driver of energetic processes is not creation of energy per se, but rather the transformation of energy from one type to another. The direction of this transformation favors an increase in entropy. In practice, this means that in natural processes energy is transformed from more concentrated forms, to less concentrated and more randomly distributed forms, for example heat.

The exact context of such changes and transformations varies from one natural science to another. Some examples include:

Physics: In physics the transformation that constitute the context is the change in position or movement of an object which is brought about through the action of a force. Thus in the context of physics energy is said to be the ability to do work, the strict mathematical definition of energy in physics is always done via the amount of work itself (done by or against specified force). Because forces are usually classified by kind (gravitational, electrostatic, etc), so are the specific forms of work they produce (or are involved in). For example, a gravitational potential energy is defined as the amount of work to elevate (or lower) a mass against a gravitational force; electrostatic energy is defined as the work done to rearrange electric charges against electric force, kinetic energy is defined as the amount of work to accelerate a body (against force of inertia) to a given velocity, etc.

Work (and energy) is, simplistically, a force multiplied by a distance (more accurately, force integrated over a certain path). Units of energy are thus exactly the same as units of work (=Joule in SI). Because work is frame dependent (= can only be defined relative to certain initial state or reference state of the system), energy also becomes frame dependent. For example, a speeding bullet has kinetic energy in the reference frame of a non-moving observer, but it has zero kinetic energy in its proper (co-moving) reference frame -- because it takes zero work to accelerate a bullet from zero speed to zero speed. Of course, the selection of a reference state (or reference frame) is completely arbitrary - and usually is dictated to maximally simplify the problem to be dealt with. However, when the total energy of a system cannot be decreased by simple choice of reference frame, then the (minimal) energy remaining in the system is associated with an invariant mass of the system. In this special frame, called the center-of-momentum frame or center-of-mass frame, total energy of the system E and its invariant mass m are related by Einstein's famous equation E=mc^2.

Chemistry: Because atoms and molecules have electrically charged particles, (electrons and protons) in them, electric forces are at work during the rearrangement of atoms (during formation or decomposition of molecules). The energy associated with this movement of charge is what we call "chemical energy".

A chemical reaction invariably absorbs or releases energy, either heat or light. A chemical transformation is possible only if so-called free energy decreases. The concept of free energy is a synthesis of energy and entropy. Free energy is a useful concept in chemistry, because energy considerations alone are not sufficient to decide the possibility of a chemical reaction. According to the second law of thermodynamics, the entropy of the universe must increase in all spontaneous processes (including chemical processes), and energy is transformed from one form to another (including from heat to any other form) so long as the second law is not violated. For example, a gas may expand and thus allow some of its heat to do work, but this is only possible because the net entropy of the universe increases due to the gas expansion, more than it decreases due to the disappearance of heat. Expansion of gas, radiation, and heat into empty space are still important processes which allow or cause the transformation of energy, in the modern universe.

The speed of a permitted spontaneous chemical reaction is determined by yet another concept: activation energy. It refers to the minimum energy E which reactant molecules must have, in order to be able to produce product molecules. At a given temperature the fraction of molecules with this energy is usually proportional to the Boltzmann's population factor of exp(-E/kT).

Biology: Energy transformation, is essential for the sustenance of life. Living organisms survive because of exchange of energy within and without; with the exchange always acting in a direction to increase the entropy of the universe, as a whole. (i.e. if the entropy of an organism decreases, the entropy of the left over energy from sunlight must increase even more). Nearly all transformations of energy in biology ultimately derive from the entropy-driven transformation of sunlight into heat . In a living organism chemical bonds are constantly broken and made to make the exchange and transformation of energy possible. These chemical bonds are most often bonds in carbohydrates, including sugars. Other chemical bonds include bonds in ATP and acetate, which in turn is derived from fats and oils . These molecules, along with oxygen, are common stores of concentrated energy for biological processes. Energy diffusion from more to less concentrated forms (net increase in entropy for the universe) is the driving force of all biological processes as all biochemical processes are a subset of chemical processes. Molecular biology and biochemistry are essentially the making and breaking of certain chemical bonds in the molecules found in biological organisms.

Energy captured by green plants from the solar radiation plays an important role for providing useful energy for us. Current research shows that 191 x 10²⁶ joules of energy is captured per year by photosynthesis.

Meteorology The Earth's weather patterns, including energy-releasing processes like lightning, hurricanes, snow avalanches, and floods, are all powered ultimately by the energy of sunlight striking the Earth. Although this amount varies a little each year, as a result of solar flares, prominences and the sunspot cycle, it has been estimated that the average total solar incoming radiation (or insolation) is 342 watts per square meter incident to the summit of the atmosphere, at the equator at midday, a figure known as the Solar Constant. Some 34% of this is immediately reflected by the planetary albedo, as a result of clouds, snowfields, and even reflected light from water, rock or vegetation. As more energy is received in the tropics than is re-radiated, whilst more energy is radiated at the poles than is received, climatic homeostasis is only maintained by a transfer of energy from the tropics to the poles. This transfer of energy is what drives the winds and the ocean currents. Like biological processes, weather processes involve turning energy from a concentrated form such as sunlight (i.e., heat radiation which occurs at the temperature of the sun, and therefore is concentrated into a few photons), ultimately into a less concentrated form, such as far infrared radiation (i.e., heat radiation at the much smaller characteristic temperatures that occur on Earth, and thus is diffused into many photons). However, energy may be temporarily locally stored during this process, and the sudden release of such stored sources is responsible for the most dramatic processes mentioned above.

Geology: volcanos, earthquakes, landslides, and tsunamis are all results of similar sudden releases of stored energy, in the crust of earth. The source of this energy is heat slowly released through the crust from the energy production of the Earth as a whole. Recent studies suggest that the Earth produces about 6.18 x 10^-12 watts per kilogram. Given the Earth's mass of about 5.97 x 10²⁴ kilograms, this means that the Earth is producing about 37 x 10¹² watts of energy per year. From the study of neutrinos radiated from the Earth (see KamLAND), scientists have recently estimated that about 24 terawatts of this energy comes from radioactive decay (principally of potassium 40, thorium 232 and uranium 238), with the remaining 12.9 terawatts coming from energies produced by the continuing gravitational sorting of the core and mantle of the earth, energies left over from the formation of the Earth, about 4.57 billion years ago.

Both energies decline over time, and based on half-life alone, it has been estimated that the current radioactive energy of the planet represents less than 1% of that which was available at the time the planet formed. As a result, geological forces of continental accretion, subduction and sea floor spreading, which release up to 90% of this available energy, were more active in the Archaean and Proterozoic periods than they are today. The remaining 10% of geological tectonic energy comes through hotspots produced by mantle plumes, resulting in shield volcanoes like Hawaii, geyser activity like Yellowstone or flood basalts like Iceland.

Tectonic process, driven by heat from the Earth's interior, metamorphose weathered rocks, and during orogeny periods, lift them up into mountain ranges. The potential energy represented by the mountain range's weight and height thus represents heat from the core of the Earth which has been partly transformed into gravitational potential energy. This potential energy may be suddenly released in landslides or tsunamis. Similarly, the energy release which drives an earthquake represents stresses in rocks that are mechanical potential energy which has been similarly stored from tectonic processes.

The remaining energy which drives the geological processes of erosion and deposition are a result of the interaction of solar energy and gravity. An estimated 23% of the total insolation is used to drive the water cycle. When water vapour condenses to fall as rain, it dissolves small amounts of carbon dioxide, making a weak acid. This acid acting upon the metallic silicates that form most rocks produces chemical weathering, removing the metals, and leading to the production of rocks and sand, carried by wind and water downslope through gravity to be deposited at the edge of continents in the sea. Physical weathering of rocks is produced by the expansion of ice crystals, left by water in the joint planes of rocks. A geologic cycle is continued when these eroded rocks are later uplifted into mountains.

Cosmology all stellar phenomena (including of course solar activity) are driven by various forms of energy release and diffusion. The source of this energy is ultimately derived either from gravitational collapse of matter which was distributed in the Big Bang, or else from fusion of lighter elements (primarily hydrogen) created in the Big Bang. These light elements were spread too fast and too thinly in the Big Bang process to be able to form the most stable and low-energy kinds of atoms, which have medium-sized atomic nuclei, like iron and nickel. The later formation of such atoms powers the energy-releasing reactions in stars.

Forms and relations between different forms

In the context of natural sciences, energy has different forms: thermal, chemical, electrical, radiant, nuclear etc. They can all be, in fact, reduced to kinetic energy or potential energy. Thus energy can be divided into two broad categories.

Kinetic

• According to kinetic theory, the microscopic kinetic energies, ε of the particles in a gas comprise the internal energy of a system. By the equipartition theorem each degree of freedom of a particle has an associated energy, , such that the energy per particle is proportional to temperature. For a monatomic gas having N particles each with three degrees of freedom, the internal energy is:

where k is the Boltzmann constant and T is absolute temperature. Whereas all internal energy is kinetic in an ideal gas, in solids half of it is stored in electromagnetic potential energy between particles. Thermal internal energy is present in all macroscopic objects in the universe. Although some heat transfer is mediated by the kinetic energy of a system's constituent particles, this kinetic energy exhibits Brownian motion, a highly disorganized state.

• Radiation energy, also known as light energy, is the energy of electromagnetic radiation. It is carried (in equal amounts) in electric and magnetic fields. It is quantized, and the spacing between allowed levels is called a photon. A quantum of energy of the electromagnetic field (energy of a photon) is equal to: where f is the frequency of the photon and h is the Planck's constant. Photons move at the speed of light and carry energy and momentum. Because energy or momentum can code information, photons can be used to transfer information .

Potential

Potential energy is stored unreleased energy (a positive quantity, like monetary savings), or else required energy (like monetary debt). This sort of energy may be positive or negative because it can represent work done on a system (against a restoring force) or work done by a system as a force result. (Negative energy is a mathematical construct in reference to another system.) For instance, using the power of a compressed spring to launch a dart uses the elastic potential energy stored within the spring. When the spring is released, this energy is converted into kinetic energy, and work is performed. There is a form of potential energy for each of the four basic forces in nature: gravity, electromagnetic, and strong and weak nuclear forces.

• Gravitational potential energy is the work of gravitational force during rearrangement of mutual positions of interacting masses - say, when masses are moved apart (such as when a crate is lifted), or closer together (as when a meteorite falls to Earth). If the masses of the objects are considered point masses, this work (thus the gravitational potential energy) is equal to: where m and M are the two masses in question, r is the distance between them, and G is the Gravitational constant. In case of small displacement h << r the above formula results in widely used E = mgh approximation.

• Electric potential energy is the work of electric forces during rearrangement of positions of charges, and also includes the common chemical potential energies (energy required to break chemical bonds or obtained from forming them). The energy released in lightning or from burning a litre of fuel oil, are some common kinds of electromagnetic potential energy. Electromagnetic potential energy is equal to: where q and Q are the electric charges on the objects in question, r is the distance between them, and ε₀ is the Electric constant of a vacuum.

• Magnetic potential energy is energy stored in a magnetic field, and is related to the relative motion of electric charges. It is related to electric potential energy and is considered a form of it, since both types of potential are mediated by the electromagnetic field. Magnetic potential energy is most familar as the type of energy storage which allows transfer of power within an electrical transformer.

• Potential thermal energy is the part of thermal energy stored in "deformation" of atomic bonds during thermal motion of atoms (as atoms oscillate around position of equilibrium they not only have kinetic energy of motion but also potential energy of displacement from equilibrium). This energy is significant portion (about half) of thermal energy for strongly-bonded systems (=solids and liquids), but much less in gasses.

• Potential chemical energy is the energy which may potentially be liberated, when the bonds of chemical structures are rearranged (energy is never stored in chemical bonds except as a negative quanity, but net energy may be released when weak chemical bonds are broken and stonger bonds are made). An example would be a system of fuel and oxygen, which stores chemical energy as compared to the products of combustion. Chemical potential energy may be either released or stored in chemical systems, such as a common rechargable battery.

• Potential elastic energy is the energy stored in the elastic nature of objects. In the ideal case, of Hooke's Law, the energy is equal to: where k is the spring constant, dependant on the individual spring, and x is the deformation of the object.

• Nuclear potential energy, along with Electric potential energy, provides the energy released from nuclear fission and nuclear fusion processes. In both cases strong nuclear forces bind nuclear particles more strongly and closely, after the reaction has completed. Weak nuclear forces (different from strong forces) provide the potential energy for certain kinds of radioactive decay, such as beta decay. Ultimately, the energy released in nuclear processes is so large that the change in mass is appreciable as being several parts per thousand in mass: where Δm is the amount of rest mass released into the surroundings as active energy (heat, light, kinetic energy), and c is the speed of light in a vacuum. Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them have less mass than if they were individually free, and this mass difference is liberated as heat and radiation in nuclear reactions.

Conservation of energy

Energy is subject to the law of conservation of energy (which is a mathematical restatement of shift symmetry of time). Thus, energy cannot be made or destroyed, it can only be converted from one form to another, that is, transformed. In practice, during any energy transformation in (macroscopic) system, some energy is converted into incoherent microscopic motion of parts of the system (which is usually called heat or thermal motion), and the entropy of the system increases. Due to mathematical impossibility to invert this process (see statistical mechanics), the efficiency of energy conversion in a macroscopic system is always less than 100%.

The first law of thermodynamics states that the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. In other words, energy is neither created nor destroyed, only converted between forms. This law is used in all branches of physics, but frequently violated for short enough periods of time during which energy can not be mathematically defined yet . Noether's theorem relates the conservation of energy to the time invariance of physical laws.

The law of conservation of energy, a fundamental principle of physics, follows from the translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. The fact that energy can not be defined for arbitrary short periods of time in quantum mechanics follows from the definition of energy operator which results mathematically in the mutual uncertainty of time and energy known as the uncertainty principle

Despite being seemingly insignificant, this principle has profound impact on processes in our Universe. It results in the existence of virtual particles which carry momentum, exchange by which with real particles is responsible for creation of all known fundamental forces (more accurately known as fundamental interactions). Virtual photons (which are simply lowest quantum mechanical energy state of photons) are also responsible for spontaneous radiative decay of exited atomic and nuclear states, for the Casimir force, for Van der Vaals bond forces and some other observable phenomena.

Conversion of energy into different forms

As a consequence of energy conservation law, one form of energy can often be readily transformed into another - for instance, a battery converts chemical energy into electrical energy. Similarly, gravitational potential energy is converted into the kinetic energy of moving water (and a turbine) in a dam, which in turn is transformed into electric energy by a generator. Similarly in the case of a chemical explosion chemical potential energy is converted to kinetic energy and heat in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at its maximum. At its lowest point the kinetic energy is at its maximum and is equal to the decrease of potential energy. If one unrealistically assumes that there is no friction, the energy will be conserved and the pendulum will continue swinging forever.

In all these cases, as long as no energy is allowed to escape from the system, the sum of all the different energies in the system remains constant, no matter how many changes take place.

In practice, available energy is rarely perfectly conserved when a system changes state; in large systems (consisting of many atoms), some energy will be converted into 'useless' (non-available) energies, such as those associated with heat. This fraction, however, may be reduced arbitrarily toward zero. In large systems with little friction (such as a planet orbiting its sun), motion may continue nearly indefinitely because useable energy is traded between usable kinetic and potential energies with so little conversion into heat. In small systems such the atom or in a vibrating molecule, where there may be no friction associated with the motion of electrons or the mututal vibration of nuclei, the possibility of indefinite motion, with perpetual conversion of kinetic and potential energy, is the case.

While energy in forms other than heat may be freely converted to other forms (including into heat) with efficiency approaching or even equaling 100%, once energy has been converted into heat, there are severe limitations in re-converting this energy into other useful forms, and efficiency never reaches 100%. If this were not so, the creation of certain kinds of perpetual motion machines (those which evolve heat, but use that heat to continue running) would be possible.

Heat, therefore, deserves to be placed in a special class of energy, which has been "degraded" by giving it access to all parts of a system. While most heat consists of kinetic and potential energies associated with atomic motion, or with certain kinds of radiant energy (i.e., electromagnetic energy with a blackbody spectrum), the energy associated with heat is in a "diffused" and non-direction form, in which the energy has spread out to occupy all of the possible states of a system which can store it. This happens at a certain equilibrium temperature, where "temperature" is a measure of energy concentration in a system. When all parts of a system reach the same temperature, the energy of heat cannot be directed into particular other kinds of energy (or used to do work), unless the system is "enlarged" in some fashion which allows the heat is allowed to diffuse into a particular direction, in which it is even less concentrated (such as when the heat is allowed to flow to a region of lower temperature). Thus we see that heat is energy which has already reached a sort of minimal concentration or diffusion in the system it is in, and is useless for doing any kind of work unless the system is opened in such a way as to let the heat have access to a larger system.

Energy is always conserved in closed systems, if heat is taken into account. But the amount of useful energy is usually not conserved, since once energy is converted to heat, it loses some of its ability to do work, and therefore its ability to be convertible to other kinds of energy.

Work

Because energy is defined in terms of work, a definition of work is crucial to the understanding of energy.

Work is a defined as a line integral of force F over distance s:

The equation above says that the work (W) is equal to the integral of the dot product of the force ( ) on a body and the infinitesimal of the body's translation ( ).

Depending on the kind of force F involved, work of this force results in corresponding kind of energy (gravitational, electrostatic, kinetic, etc).

For example, the gravitational force F=-mg acting on a mass m when the mass is elevated from some height h₁ (reference height) to the height h₂ is therefore:

W = -mg(h₁ - h₂)= mgh₂ - mgh₁