Editing Zero-point energy (section)

=== Single heat baths ===
In 1951 [[Herbert Callen|Callen]] and Welton<ref name="ReferenceB"/> proved the quantum [[fluctuation-dissipation theorem]] (FDT) which was originally formulated in classical form by [[Harry Nyquist|Nyquist]] (1928)<ref name="ReferenceC"/> as an explanation for observed [[Johnson noise]]<ref name="ReferenceD"/> in electric circuits. Fluctuation-dissipation theorem showed that when something dissipates energy, in an effectively irreversible way, a connected heat bath must also fluctuate. The fluctuations and the dissipation go hand in hand; it is impossible to have one without the other. The implication of FDT being that the vacuum could be treated as a heat bath coupled to a dissipative force and as such energy could, in part, be extracted from the vacuum for potentially useful work.{{sfnp|Milonni|1994|p=54}} Such a theory has met with resistance: Macdonald (1962)<ref>{{cite journal |last1=MacDonald |first1=D. K. C. |date=1962 |title=On Brownian Movement and irreversibility |journal=Physica |volume=28 |issue=4 |pages=409–416 |bibcode=1962Phy....28..409M |doi=10.1016/0031-8914(62)90019-8}}</ref> and Harris (1971)<ref>{{cite journal|last1=Harris|first1=I. A.|title=Zero-point fluctuations and thermal-noise standards|journal=Electron. Lett.|date=1971|volume=7|issue=7|pages=148–149|doi=10.1049/el:19710095|bibcode=1971ElL.....7..148H}}</ref> claimed that extracting power from the zero-point energy to be impossible, so FDT could not be true. Grau and Kleen (1982)<ref>{{cite journal|last1=Grau|first1=G.|last2=Kleen|first2=W.|title=Comments on zero-point energy, quantum noise and spontaneous-emission noise|journal=Solid-State Electronics|date=1982|volume=25|issue=8|pages=749–751|doi=10.1016/0038-1101(82)90204-0|bibcode=1982SSEle..25..749G}}</ref> and Kleen (1986),<ref>{{Cite book|last1=Kleen|first1=W.|title=Noise in Physical Systems and 1/F Noise 1985|chapter=Thermal noise and zero-point-energy|date=1985|pages=331–332|doi=10.1016/B978-0-444-86992-0.50072-2|isbn=9780444869920|url=https://archive.org/details/noiseinphysicals00dami|url-access=limited}}</ref> argued that the Johnson noise of a resistor connected to an antenna must satisfy Planck's thermal radiation formula, thus the noise must be zero at zero temperature and FDT must be invalid. Kiss (1988)<ref>{{cite journal|last1=Kiss|first1=L. B.|title=To the problem of zero-point energy and thermal noise|journal=Solid State Communications|date=1988|volume=67|issue=7|pages=749–751|doi=10.1016/0038-1098(88)91020-4|bibcode=1988SSCom..67..749K}}</ref> pointed out that the existence of the zero-point term may indicate that there is a renormalization problem—i.e., a mathematical artifact—producing an unphysical term that is not actually present in measurements (in analogy with renormalization problems of ground states in quantum electrodynamics). Later, Abbott et al. (1996) arrived at a different but unclear conclusion that "zero-point energy is infinite thus it should be renormalized but not the 'zero-point fluctuations'".{{sfnp|Abbott et al.|1996}} Despite such criticism, FDT has been shown to be true experimentally under certain quantum, non-classical conditions. Zero-point fluctuations can, and do, contribute towards systems which dissipate energy.<ref name="cloudfront.escholarship.org"/> A paper by Armen Allahverdyan and Theo Nieuwenhuizen in 2000 showed the feasibility of extracting zero-point energy for useful work from a single bath, without contradicting the [[laws of thermodynamics]], by exploiting certain quantum mechanical properties.<ref name=Allahverdyan-2000/>

There have been a growing number of papers showing that in some instances the classical laws of thermodynamics, such as limits on the Carnot efficiency, can be violated by exploiting negative entropy of quantum fluctuations.{{sfnp|Scully et al.|2003}}{{sfnp|Scully|2001}}<ref>{{cite journal |last1=Galve |first1=Fernando |last2=Lutz |first2=Eric |title=Nonequilibrium thermodynamic analysis of squeezing |journal=Physical Review A |date=2009 |volume=79 |issue=5 |page=055804 |doi=10.1103/PhysRevA.79.055804 |bibcode=2009PhRvA..79e5804G}}</ref><ref>{{cite journal |last1=Dillenschneider |first1=R. |last2=Lutz |first2=E. |title=Energetics of quantum correlations |journal=EPL |date=2009 |volume=88 |issue=5 |page=50003 |doi=10.1209/0295-5075/88/50003 |bibcode=2009EL.....8850003D |arxiv=0803.4067|s2cid=119262651 }}</ref><ref>{{cite journal |last1=Huang |first1=X. L. |last2=Wang |first2=Tao |last3=Yi |first3=X. X. |title=Effects of reservoir squeezing on quantum systems and work extraction |journal=Physical Review E |date=2012 |volume=86 |issue=5 |page=051105 |doi=10.1103/PhysRevE.86.051105 |pmid=23214736 |bibcode=2012PhRvE..86e1105H|doi-access=free }}</ref><ref>{{cite journal|last1=Boukobza|first1=E.|last2=Ritsch|first2=H.|title=Breaking the Carnot limit without violating the second law: A thermodynamic analysis of off-resonant quantum light generation|journal=Physical Review A|date=2013|volume=87|issue=6|page=063845|doi= 10.1103/PhysRevA.87.063845|bibcode= 2013PhRvA..87f3845B}}</ref>{{sfnp|Roßnagel et al.|2014}}{{sfnp|Correa et al.|2014}}<ref>{{cite journal|last1=Abah|first1=Obinna|last2=Lutz|first2=Eric|title=Efficiency of heat engines coupled to nonequilibrium reservoirs|journal=EPL|year=2014|volume=106|issue=2|page=20001|doi= 10.1209/0295-5075/106/20001|arxiv= 1303.6558|bibcode= 2014EL....10620001A|s2cid=118468331}}</ref><ref>{{cite journal|last1=Gardas|first1=Bartłomiej|last2=Deffner|first2=Sebastian|last3=Saxena|first3=Avadh|title=Non-hermitian quantum thermodynamics|journal=Scientific Reports|year=2016|volume=6|page=23408|doi= 10.1038/srep23408|pmid= 27003686|pmc= 4802220|arxiv= 1511.06256|bibcode= 2016NatSR...623408G}}</ref>

Despite efforts to reconcile quantum mechanics and thermodynamics over the years, their compatibility is still an open fundamental problem. The full extent that quantum properties can alter classical thermodynamic bounds is unknown<ref>{{cite book|last1=Gemmer |first1=Jochen|last2=Michel |first2=M.|last3=Mahler|first3=Günter|title=Quantum Thermodynamics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems|date=2009|publisher=Springer|isbn=978-3-540-70510-9|doi=10.1007/978-3-540-70510-9|url=https://cds.cern.ch/record/1339164}}</ref>