Editing Entropy (section)

== Second law of thermodynamics ==
The [[second law of thermodynamics]] requires that, in general, the total entropy of any system does not decrease other than by increasing the entropy of some other system. Hence, in a system isolated from its environment, the entropy of that system tends not to decrease. It follows that heat cannot flow from a colder body to a hotter body without the application of work to the colder body. Secondly, it is impossible for any device operating on a cycle to produce net work from a single temperature reservoir; the production of net work requires flow of heat from a hotter reservoir to a colder reservoir, or a single expanding reservoir undergoing [[adiabatic cooling]], which performs [[adiabatic process|adiabatic work]]. As a result, there is no possibility of a [[perpetual motion]] machine. It follows that a reduction in the increase of entropy in a specified process, such as a [[chemical reaction]], means that it is energetically more efficient.

It follows from the second law of thermodynamics that the entropy of a system that is not isolated may decrease. An [[air conditioner]], for example, may cool the air in a room, thus reducing the entropy of the air of that system. The heat expelled from the room (the system), which the air conditioner transports and discharges to the outside air, always makes a bigger contribution to the entropy of the environment than the decrease of the entropy of the air of that system. Thus, the total of entropy of the room plus the entropy of the environment increases, in agreement with the second law of thermodynamics.

In mechanics, the second law in conjunction with the [[fundamental thermodynamic relation]] places limits on a system's ability to do [[work (thermodynamics)|useful work]].<ref name="Daintith">{{Cite book|last=Daintith| first=John|title=Oxford Dictionary of Physics|publisher=Oxford University Press|year=2005|isbn=978-0-19-280628-4}}</ref> The entropy change of a system at temperature <math display="inline">T</math> absorbing an infinitesimal amount of heat <math display="inline">\delta q</math> in a reversible way, is given by <math display="inline">\delta q / T</math>. More explicitly, an energy <math display="inline">T_R S</math> is not available to do useful work, where <math display="inline">T_R</math> is the temperature of the coldest accessible reservoir or heat sink external to the system. For further discussion, see ''[[Exergy]]''.

Statistical mechanics demonstrates that entropy is governed by probability, thus allowing for a decrease in disorder even in an isolated system. Although this is possible, such an event has a small probability of occurring, making it unlikely.<ref>{{Cite journal |title=Entropy production theorems and some consequences|pages=1–10 |journal=Physical Review E |volume=80 |issue=1 |doi=10.1103/PhysRevE.80.011117 |pmid=19658663 |year=2009 |last1=Saha |first1=Arnab |last2=Lahiri |first2=Sourabh |last3=Jayannavar |first3=A. M. |bibcode=2009PhRvE..80a1117S |arxiv=0903.4147 |s2cid=22204063 }}</ref>

The applicability of a second law of thermodynamics is limited to systems in or sufficiently near [[thermodynamic equilibrium|equilibrium state]], so that they have defined entropy.<ref>{{cite journal|last1=Martyushev|first1=L. M.|last2=Seleznev|first2=V. D.|title=The restrictions of the maximum entropy production principle|journal=Physica A: Statistical Mechanics and Its Applications|year=2014|volume=410|doi=10.1016/j.physa.2014.05.014|pages=17–21|arxiv=1311.2068|bibcode=2014PhyA..410...17M|s2cid=119224112}}</ref> Some inhomogeneous systems out of thermodynamic equilibrium still satisfy the hypothesis of [[Thermodynamic equilibrium#local and global equilibrium|local thermodynamic equilibrium]], so that entropy density is locally defined as an intensive quantity. For such systems, there may apply a principle of maximum time rate of entropy production.<ref>{{cite book|last1=Ziegler|first1=H.|title=An Introduction to Thermomechanics|date=1983|location=North Holland, Amsterdam.}}</ref><ref>{{cite journal|last1=Onsager|first1=Lars|title=Reciprocal Relations in Irreversible Processes|journal=Phys. Rev. |volume=37|issue=4|page=405|year=1931|doi=10.1103/PhysRev.37.405|bibcode=1931PhRv...37..405O|doi-access=free}}</ref> It states that such a system may evolve to a steady state that maximises its time rate of entropy production. This does not mean that such a system is necessarily always in a condition of maximum time rate of entropy production; it means that it may evolve to such a steady state.<ref>{{cite book|last1=Kleidon|first1=A.|last2=et.|first2=al.|title=Non-equilibrium Thermodynamics and the Production of Entropy|date=2005|publisher=Springer|location=Heidelberg}}</ref><ref>{{cite journal|last1=Belkin|first1=Andrey|last2=et.|first2=al.|title=Self-assembled wiggling nano-structures and the principle of maximum entropy production|journal=Scientific Reports |year=2015|doi=10.1038/srep08323|pmid=25662746|pmc=4321171|volume=5|issue=1 |pages=8323|bibcode=2015NatSR...5.8323B}}</ref>