In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is related to the number Ω of microscopic configurations that are consistent with the macroscopic quantities that characterize the system. Under the assumption that each microstate is probable, the entropy S is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB. Formally, S = k B ln Ω. Macroscopic systems have a large number Ω of possible microscopic configurations. For example, the entropy of an ideal gas is proportional to the number of gas molecules N. Twenty liters of gas at room temperature and atmospheric pressure has N ≈ 6×1023. At equilibrium, each of the Ω ≈ eN configurations can be regarded as random and likely; the second law of thermodynamics states. Such systems spontaneously evolve towards the state with maximum entropy. Non-isolated systems may lose entropy, provided their environment's entropy increases by at least that amount so that the total entropy increases.
Entropy is a function of the state of the system, so the change in entropy of a system is determined by its initial and final states. In the idealization that a process is reversible, the entropy does not change, while irreversible processes always increase the total entropy; because it is determined by the number of random microstates, entropy is related to the amount of additional information needed to specify the exact physical state of a system, given its macroscopic specification. For this reason, it is said that entropy is an expression of the disorder, or randomness of a system, or of the lack of information about it; the concept of entropy plays a central role in information theory. Boltzmann's constant, therefore entropy, have dimensions of energy divided by temperature, which has a unit of joules per kelvin in the International System of Units; the entropy of a substance is given as an intensive property—either entropy per unit mass or entropy per unit amount of substance. The French mathematician Lazare Carnot proposed in his 1803 paper Fundamental Principles of Equilibrium and Movement that in any machine the accelerations and shocks of the moving parts represent losses of moment of activity.
In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy. Building on this work, in 1824 Lazare's son Sadi Carnot published Reflections on the Motive Power of Fire which posited that in all heat-engines, whenever "caloric" falls through a temperature difference, work or motive power can be produced from the actions of its fall from a hot to cold body, he made the analogy with that of. This was an early insight into the second law of thermodynamics. Carnot based his views of heat on the early 18th century "Newtonian hypothesis" that both heat and light were types of indestructible forms of matter, which are attracted and repelled by other matter, on the contemporary views of Count Rumford who showed that heat could be created by friction as when cannon bores are machined. Carnot reasoned that if the body of the working substance, such as a body of steam, is returned to its original state at the end of a complete engine cycle, that "no change occurs in the condition of the working body".
The first law of thermodynamics, deduced from the heat-friction experiments of James Joule in 1843, expresses the concept of energy, its conservation in all processes. In the 1850s and 1860s, German physicist Rudolf Clausius objected to the supposition that no change occurs in the working body, gave this "change" a mathematical interpretation by questioning the nature of the inherent loss of usable heat when work is done, e.g. heat produced by friction. Clausius described entropy as the transformation-content, i.e. dissipative energy use, of a thermodynamic system or working body of chemical species during a change of state. This was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass. Scientists such as Ludwig Boltzmann, Josiah Willard Gibbs, James Clerk Maxwell gave entropy a statistical basis. In 1877 Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles, in which he defined entropy to be proportional to the natural logarithm of the number of microstates such a gas could occupy.
Henceforth, the essential problem in statistical thermodynamics, i.e. according to Erwin Schrödinger, has been to determine the distribution of a given amount of energy E over N identical systems. Carathéodory linked entropy with a mathematical definition of irreversibility, in terms of trajectories and integrability. There are two related definitions of entropy: the thermodynamic definition and the statistical mechanics definition; the classical thermodynamics definition developed first. In the classical thermodynamics viewpoint, the system is composed of large numbers of constituents and the state of the system is described by the average thermodynamic properties of those constituents.
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the SI unit of energy is the joule, the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton. Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field, the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, the thermal energy due to an object's temperature. Mass and energy are related. Due to mass–energy equivalence, any object that has mass when stationary has an equivalent amount of energy whose form is called rest energy, any additional energy acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.
Living organisms require exergy to stay alive, such as the energy. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy; the processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth. The total energy of a system can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways. Kinetic energy is determined by the movement of an object – or the composite motion of the components of an object – and potential energy reflects the potential of an object to have motion, is a function of the position of an object within a field or may be stored in the field itself. While these two categories are sufficient to describe all forms of energy, it is convenient to refer to particular combinations of potential and kinetic energy as its own form. For example, macroscopic mechanical energy is the sum of translational and rotational kinetic and potential energy in a system neglects the kinetic energy due to temperature, nuclear energy which combines utilize potentials from the nuclear force and the weak force), among others.
The word energy derives from the Ancient Greek: translit. Energeia, lit.'activity, operation', which appears for the first time in the work of Aristotle in the 4th century BC. In contrast to the modern definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness and pleasure. In the late 17th century, Gottfried Leibniz proposed the idea of the Latin: vis viva, or living force, which defined as the product of the mass of an object and its velocity squared. To account for slowing due to friction, Leibniz theorized that thermal energy consisted of the random motion of the constituent parts of matter, although it would be more than a century until this was accepted; the modern analog of this property, kinetic energy, differs from vis viva only by a factor of two. In 1807, Thomas Young was the first to use the term "energy" instead of vis viva, in its modern sense. Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, in 1853, William Rankine coined the term "potential energy".
The law of conservation of energy was first postulated in the early 19th century, applies to any isolated system. It was argued for some years whether heat was a physical substance, dubbed the caloric, or a physical quantity, such as momentum. In 1845 James Prescott Joule discovered the generation of heat; these developments led to the theory of conservation of energy, formalized by William Thomson as the field of thermodynamics. Thermodynamics aided the rapid development of explanations of chemical processes by Rudolf Clausius, Josiah Willard Gibbs, Walther Nernst, it led to a mathematical formulation of the concept of entropy by Clausius and to the introduction of laws of radiant energy by Jožef Stefan. According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time. Thus, since 1918, theorists have understood that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time.
In 1843, James Prescott Joule independently discovered the mechanical equivalent in a series of experiments. The most famous of them used the "Joule apparatus": a descending weight, attached to a string, caused rotation of a paddle immersed in water insulated from heat transfer, it showed that the gravitational potential energy lost by the weight in descending was equal to the internal energy gained by the water through friction with the paddle. In the International System of Units, the unit of energy is the joule, named after James Prescott Joule, it is a derived unit. It is equal to the energy expended in applying a force of one newton through a distance of one metre; however energy is expressed in many other units not part of the SI, such as ergs, British Thermal Units, kilowatt-hours and kilocalories, which require a conversion factor when expressed in SI units. The SI unit of energy rate is the watt, a joule per second. Thus, one joule is one watt-second, 3600 joules equal one wa