Editing Energy (section)

== Thermodynamics ==

=== Internal energy ===
[[Internal energy]] is the sum of all microscopic forms of energy of a system. It is the energy needed to create the system. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometric aspects, as well as the motion of the particles, in form of kinetic energy. Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value, which is impossible to determine with thermodynamics alone.<ref name=klotz>I. Klotz, R. Rosenberg, ''Chemical Thermodynamics – Basic Concepts and Methods'', 7th ed., Wiley (2008), p. 39</ref>

=== First law of thermodynamics ===
The [[first law of thermodynamics]] asserts that the total energy of a system and its surroundings (but not necessarily [[thermodynamic free energy]]) is always conserved<ref name="KK">{{Cite book|author=Kittel and Kroemer|title=Thermal Physics |year=1980|publisher=W.H. Freeman |location=New York| isbn=978-0-7167-1088-2}}</ref> and that heat flow is a form of energy transfer. For homogeneous systems, with a well-defined temperature and pressure, a commonly used corollary of the first law is that, for a system subject only to [[pressure]] forces and heat transfer (e.g., a cylinder-full of gas) without chemical changes, the differential change in the internal energy of the system (with a ''gain'' in energy signified by a positive quantity) is given as
: <math>\mathrm{d}E = T\mathrm{d}S - P\mathrm{d}V\,,</math>
where the first term on the right is the heat transferred into the system, expressed in terms of [[temperature]] ''T'' and [[entropy]] ''S'' (in which entropy increases and its change d''S'' is positive when heat is added to the system), and the last term on the right hand side is identified as work done on the system, where pressure is ''P'' and volume ''V'' (the negative sign results since compression of the system requires work to be done on it and so the volume change, d''V'', is negative when work is done on the system).

This equation is highly specific, ignoring all chemical, electrical, nuclear, and gravitational forces, effects such as [[advection]] of any form of energy other than heat and ''PV''-work. The general formulation of the first law (i.e., conservation of energy) is valid even in situations in which the system is not homogeneous. For these cases the change in internal energy of a ''closed'' system is expressed in a general form by
: <math>\mathrm{d}E=\delta Q+\delta W</math>
where <math>\delta Q</math> is the heat supplied to the system and <math>\delta W</math> is the work applied to the system.

=== Equipartition of energy ===
The energy of a mechanical [[harmonic oscillator]] (a mass on a spring) is alternately [[kinetic energy|kinetic]] and [[potential energy]]. At two points in the oscillation [[Frequency|cycle]] it is entirely kinetic, and at two points it is entirely potential. Over a whole cycle, or over many cycles, average energy is equally split between kinetic and potential. This is an example of the [[equipartition principle]]: the total energy of a system with many degrees of freedom is equally split among all available degrees of freedom, on average.

This principle is vitally important to understanding the behavior of a quantity closely related to energy, called [[entropy]]. Entropy is a measure of evenness of a [[distribution (mathematics)|distribution]] of energy between parts of a system. When an isolated system is given more degrees of freedom (i.e., given new available [[energy state]]s that are the same as existing states), then total energy spreads over all available degrees equally without distinction between "new" and "old" degrees. This mathematical result is part of the [[second law of thermodynamics]]. The second law of thermodynamics is simple only for systems which are near or in a physical [[equilibrium state]]. For non-equilibrium systems, the laws governing the systems' behavior are still debatable. One of the guiding principles for these systems is the principle of [[principle of maximum entropy|maximum entropy production]].<ref>{{cite journal|last1=Onsager|first1=L.|title=Reciprocal relations in irreversible processes.|journal=Phys. Rev. |volume=37|issue=4|date=1931|pages=405–26|bibcode=1931PhRv...37..405O|doi=10.1103/PhysRev.37.405|doi-access=free}}</ref><ref>{{cite journal |last1=Martyushev |first1=L. M. |last2=Seleznev |first2=V. D. |date=2006 |title=Maximum entropy production principle in physics, chemistry and biology |journal=Physics Reports |volume=426 |issue=1 |pages=1–45 |bibcode=2006PhR...426....1M |doi=10.1016/j.physrep.2005.12.001}}</ref> It states that nonequilibrium systems behave in such a way as to maximize their entropy production.<ref>{{cite journal|last1=Belkin|first1=A.|last2=et.|first2=al.|title=Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production|journal=Sci. Rep. |volume=5|pages=8323|date=2015|issue=1 |doi=10.1038/srep08323|pmid=25662746|pmc=4321171|bibcode=2015NatSR...5.8323B}}</ref>