Physics:Quantum heat engines - Revision history

WikiHarold: Fix final Quantum red link source

2026-05-24T00:07:45Z

Fix final Quantum red link source

← Older revision		Revision as of 00:07, 24 May 2026
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	Quantum devices operate either continuously or via reciprocating cycles. Continuous devices include solar cells, thermoelectric devices (outputting current), and lasers (outputting coherent light). Continuous refrigerators use optical pumping or laser cooling.<ref name="NareviciusBannerman2009">{{cite journal\|last1=Narevicius\|first1=Edvardas\|last2=Bannerman\|first2=S Travis\|last3=Raizen\|first3=Mark G\|title=Single-photon molecular cooling\|journal=New Journal of Physics\|volume=11\|issue=5\|year=2009\|article-number=055046\|issn=1367-2630\|doi=10.1088/1367-2630/11/5/055046\|doi-access=free\|bibcode=2009NJPh...11e5046N\|arxiv=0808.1383}}</ref><ref name="am1">{{cite journal\|last1=Kosloff\|first1=Ronnie\|last2=Levy\|first2=Amikam\|title=Quantum Heat Engines and Refrigerators: Continuous Devices\|journal=Annual Review of Physical Chemistry\|volume=65\|issue=1\|year=2014\|pages=365–393\|issn=0066-426X\|doi=10.1146/annurev-physchem-040513-103724\|pmid=24689798\|arxiv=1310.0683\|bibcode=2014ARPC...65..365K\|s2cid=25266545}}</ref> Reciprocating devices, such as four-stroke or two-stroke machines, mimic classical engines with non-commuting strokes. Common cycles include the Carnot cycle<ref name="geva2">{{cite journal\|last1=Geva\|first1=Eitan\|last2=Kosloff\|first2=Ronnie\|title=A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid\|journal=The Journal of Chemical Physics\|volume=96\|issue=4\|year=1992\|pages=3054–3067\|issn=0021-9606\|doi=10.1063/1.461951\|bibcode=1992JChPh..96.3054G}}</ref><ref name="bender">{{cite journal\|last1=Bender\|first1=Carl M\|last2=Brody\|first2=Dorje C\|last3=Meister\|first3=Bernhard K\|title=Quantum mechanical Carnot engine\|journal=Journal of Physics A: Mathematical and General\|volume=33\|issue=24\|year=2000\|pages=4427–4436\|issn=0305-4470\|doi=10.1088/0305-4470/33/24/302\|arxiv=quant-ph/0007002\|bibcode=2000JPhA...33.4427B\|s2cid=5335}}</ref> and Otto cycle.<ref name="tova">{{cite journal\|last1=Feldmann\|first1=Tova\|last2=Kosloff\|first2=Ronnie\|title=Performance of discrete heat engines and heat pumps in finite time\|journal=Physical Review E\|volume=61\|issue=5\|year=2000\|pages=4774–4790\|issn=1063-651X\|doi=10.1103/PhysRevE.61.4774\|pmid=11031518\|bibcode=2000PhRvE..61.4774F\|arxiv=physics/0003007\|s2cid=2277942}}</ref> These cycles yield equations of motion for the working medium and heat flux.		Quantum devices operate either continuously or via reciprocating cycles. Continuous devices include solar cells, thermoelectric devices (outputting current), and lasers (outputting coherent light). Continuous refrigerators use optical pumping or laser cooling.<ref name="NareviciusBannerman2009">{{cite journal\|last1=Narevicius\|first1=Edvardas\|last2=Bannerman\|first2=S Travis\|last3=Raizen\|first3=Mark G\|title=Single-photon molecular cooling\|journal=New Journal of Physics\|volume=11\|issue=5\|year=2009\|article-number=055046\|issn=1367-2630\|doi=10.1088/1367-2630/11/5/055046\|doi-access=free\|bibcode=2009NJPh...11e5046N\|arxiv=0808.1383}}</ref><ref name="am1">{{cite journal\|last1=Kosloff\|first1=Ronnie\|last2=Levy\|first2=Amikam\|title=Quantum Heat Engines and Refrigerators: Continuous Devices\|journal=Annual Review of Physical Chemistry\|volume=65\|issue=1\|year=2014\|pages=365–393\|issn=0066-426X\|doi=10.1146/annurev-physchem-040513-103724\|pmid=24689798\|arxiv=1310.0683\|bibcode=2014ARPC...65..365K\|s2cid=25266545}}</ref> Reciprocating devices, such as four-stroke or two-stroke machines, mimic classical engines with non-commuting strokes. Common cycles include the Carnot cycle<ref name="geva2">{{cite journal\|last1=Geva\|first1=Eitan\|last2=Kosloff\|first2=Ronnie\|title=A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid\|journal=The Journal of Chemical Physics\|volume=96\|issue=4\|year=1992\|pages=3054–3067\|issn=0021-9606\|doi=10.1063/1.461951\|bibcode=1992JChPh..96.3054G}}</ref><ref name="bender">{{cite journal\|last1=Bender\|first1=Carl M\|last2=Brody\|first2=Dorje C\|last3=Meister\|first3=Bernhard K\|title=Quantum mechanical Carnot engine\|journal=Journal of Physics A: Mathematical and General\|volume=33\|issue=24\|year=2000\|pages=4427–4436\|issn=0305-4470\|doi=10.1088/0305-4470/33/24/302\|arxiv=quant-ph/0007002\|bibcode=2000JPhA...33.4427B\|s2cid=5335}}</ref> and Otto cycle.<ref name="tova">{{cite journal\|last1=Feldmann\|first1=Tova\|last2=Kosloff\|first2=Ronnie\|title=Performance of discrete heat engines and heat pumps in finite time\|journal=Physical Review E\|volume=61\|issue=5\|year=2000\|pages=4774–4790\|issn=1063-651X\|doi=10.1103/PhysRevE.61.4774\|pmid=11031518\|bibcode=2000PhRvE..61.4774F\|arxiv=physics/0003007\|s2cid=2277942}}</ref> These cycles yield equations of motion for the working medium and heat flux.
	=== Reciprocating ===		=== Reciprocating ===
	Researchers studied quantum versions of thermodynamic cycles, including the Carnot cycle,<ref name="geva2" /><ref name="bender" /><ref name="QuanLiu2007">{{cite journal\|last1=Quan\|first1=H. T.\|last2=Liu\|first2=Yu-xi\|last3=Sun\|first3=C. P.\|last4=Nori\|first4=Franco\|title=Quantum thermodynamic cycles and quantum heat engines\|journal=Physical Review E\|volume=76\|issue=3\|article-number=031105\|year=2007\|issn=1539-3755\|doi=10.1103/PhysRevE.76.031105\|pmid=17930197\|bibcode=2007PhRvE..76c1105Q\|arxiv=quant-ph/0611275\|s2cid=3009953}}</ref> Stirling cycle,<ref name="WuChen1998">{{cite journal\|last1=Wu\|first1=F.\|last2=Chen\|first2=L.\|last3=Sun\|first3=F.\|last4=Wu\|first4=C.\|last5=Zhu\|first5=Yonghong\|title=Performance and optimization criteria for forward and reverse quantum Stirling cycles\|journal=Energy Conversion and Management\|volume=39\|issue=8\|year=1998\|pages=733–739\|issn=0196-8904\|doi=10.1016/S0196-8904(97)10037-1\|bibcode=1998ECM....39..733W }}</ref> and Otto cycle.<ref name="tova" /><ref name="Kieu2006">{{cite journal\|last1=Kieu\|first1=T. D.\|title=Quantum heat engines, the second law and Maxwell's daemon\|journal=The European Physical Journal D\|volume=39\|issue=1\|year=2006\|pages=115–128\|issn=1434-6060\|doi=10.1140/epjd/e2006-00075-5\|bibcode=2006EPJD...39..115K\|arxiv=quant-ph/0311157\|s2cid=119382163}}</ref> The Otto cycle serves as a model for other reciprocating cycles. [[File:Q-otto-cycle.pdf\|thumb\|Quantum Otto cycle in the Entropy <math>\Omega</math> plane, showing energy entropy and ~~[[Physics:~~Von Neumann entropy~~\|Von Neumann entropy]]~~. <math>\Omega</math> represents the externally controlled internal frequency, mimicking inverse volume in the Otto cycle. Red and blue lines indicate hot and cold isochores. The cycle represents a heat pump.]] The Otto cycle consists of four segments:		Researchers studied quantum versions of thermodynamic cycles, including the Carnot cycle,<ref name="geva2" /><ref name="bender" /><ref name="QuanLiu2007">{{cite journal\|last1=Quan\|first1=H. T.\|last2=Liu\|first2=Yu-xi\|last3=Sun\|first3=C. P.\|last4=Nori\|first4=Franco\|title=Quantum thermodynamic cycles and quantum heat engines\|journal=Physical Review E\|volume=76\|issue=3\|article-number=031105\|year=2007\|issn=1539-3755\|doi=10.1103/PhysRevE.76.031105\|pmid=17930197\|bibcode=2007PhRvE..76c1105Q\|arxiv=quant-ph/0611275\|s2cid=3009953}}</ref> Stirling cycle,<ref name="WuChen1998">{{cite journal\|last1=Wu\|first1=F.\|last2=Chen\|first2=L.\|last3=Sun\|first3=F.\|last4=Wu\|first4=C.\|last5=Zhu\|first5=Yonghong\|title=Performance and optimization criteria for forward and reverse quantum Stirling cycles\|journal=Energy Conversion and Management\|volume=39\|issue=8\|year=1998\|pages=733–739\|issn=0196-8904\|doi=10.1016/S0196-8904(97)10037-1\|bibcode=1998ECM....39..733W }}</ref> and Otto cycle.<ref name="tova" /><ref name="Kieu2006">{{cite journal\|last1=Kieu\|first1=T. D.\|title=Quantum heat engines, the second law and Maxwell's daemon\|journal=The European Physical Journal D\|volume=39\|issue=1\|year=2006\|pages=115–128\|issn=1434-6060\|doi=10.1140/epjd/e2006-00075-5\|bibcode=2006EPJD...39..115K\|arxiv=quant-ph/0311157\|s2cid=119382163}}</ref> The Otto cycle serves as a model for other reciprocating cycles. [[File:Q-otto-cycle.pdf\|thumb\|Quantum Otto cycle in the Entropy <math>\Omega</math> plane, showing energy entropy and Von Neumann entropy. <math>\Omega</math> represents the externally controlled internal frequency, mimicking inverse volume in the Otto cycle. Red and blue lines indicate hot and cold isochores. The cycle represents a heat pump.]] The Otto cycle consists of four segments:
	* Segment <math>A \rightarrow B</math>: Isomagnetic or isochoric process, partial equilibration with the cold reservoir, described by propagator <math>U_\text{c}</math>.		* Segment <math>A \rightarrow B</math>: Isomagnetic or isochoric process, partial equilibration with the cold reservoir, described by propagator <math>U_\text{c}</math>.
	* Segment <math>B \rightarrow C</math>: Magnetization or adiabatic compression, expanding energy level gaps in the Hamiltonian, described by propagator <math>U_\text{ch}</math>.		* Segment <math>B \rightarrow C</math>: Magnetization or adiabatic compression, expanding energy level gaps in the Hamiltonian, described by propagator <math>U_\text{ch}</math>.

WikiHarold: Remove imported red links from Quantum page

2026-05-23T23:47:33Z

Remove imported red links from Quantum page

← Older revision		Revision as of 23:47, 23 May 2026
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	Scovil and Schulz-DuBois first connected the [[Physics:Quantum amplifier\|quantum amplifier]] to [[Biography:Nicolas Léonard Sadi Carnot\|Carnot]] efficiency in 1959, building a quantum heat engine with a 3-level maser.<ref name="scovil59">{{cite journal \|last1=Scovil \|first1=H. E. D. \|last2=Schulz-DuBois \|first2=E. O. \|title=Three-Level Masers as Heat Engines \|journal=Physical Review Letters \|volume=2 \|issue=6 \|year=1959 \|pages=262–263 \|issn=0031-9007 \|doi=10.1103/PhysRevLett.2.262 \|bibcode=1959PhRvL...2..262S}}</ref> Geusic, Schulz-DuBois, De Grasse, and Scovil proposed quantum refrigerators, which pump heat from a cold to a hot reservoir using power, in the same year.<ref name="GeusicBois1959">{{cite journal \|last1=Geusic \|first1=J. E. \|last2=Bois \|first2=E. O. Schulz-Du \|last3=De Grasse \|first3=R. W. \|last4=Scovil \|first4=H. E. D. \|title=Three Level Spin Refrigeration and Maser Action at 1500 mc/sec \|journal=Journal of Applied Physics \|volume=30 \|issue=7 \|year=1959 \|pages=1113–1114 \|issn=0021-8979 \|doi=10.1063/1.1776991 \|bibcode=1959JAp....30.1113G}}</ref> Wineland and Hänsch suggested laser-driven processes, termed optical pumping or laser cooling.<ref name="wineland">{{cite journal \|author1=D. J. Wineland \|author2=H. Dehmelt \|title=Proposed 10<sup>14</sup>Δν < ν Laser Fluorescence Spectroscopy on Tl<sup>+</sup> Mono-Ion Oscillator III \|journal=Bull. Am. Phys. Soc. \|volume=20 \|page=637 \|year=1975 \|url=https://tf.nist.gov/general/pdf/2208.pdf}}</ref><ref name="HänschSchawlow1975">{{cite journal \|last1=Hänsch \|first1=T. W. \|last2=Schawlow \|first2=A. L. \|title=Cooling of gases by laser radiation \|journal=Optics Communications \|volume=13 \|issue=1 \|year=1975 \|pages=68–69 \|issn=0030-4018 \|doi=10.1016/0030-4018(75)90159-5 \|doi-access=free \|bibcode=1975OptCo..13...68H}}</ref><ref name="LetokhovMinogin1976">{{cite journal \|last1=Letokhov \|first1=V. S. \|last2=Minogin \|first2=V. G. \|last3=Pavlik \|first3=B. D. \|title=Cooling and trapping of atoms and molecules by a resonant laser field \|journal=Optics Communications \|volume=19 \|issue=1 \|year=1976 \|pages=72–75 \|issn=0030-4018 \|doi=10.1016/0030-4018(76)90388-6 \|bibcode=1976OptCo..19...72L}}</ref> Alicki reported that heat engines and refrigerators can function at the single-particle scale, necessitating [[Physics:Quantum thermodynamics\|quantum thermodynamics]].<ref name="alicki1">{{cite journal \|last1=Alicki \|first1=R. \|title=The quantum open system as a model of the heat engine \|journal=Journal of Physics A: Mathematical and General \|volume=12 \|issue=5 \|year=1979 \|pages=L103–L107 \|issn=0305-4470 \|doi=10.1088/0305-4470/12/5/007 \|bibcode=1979JPhA...12L.103A}}</ref>		Scovil and Schulz-DuBois first connected the [[Physics:Quantum amplifier\|quantum amplifier]] to [[Biography:Nicolas Léonard Sadi Carnot\|Carnot]] efficiency in 1959, building a quantum heat engine with a 3-level maser.<ref name="scovil59">{{cite journal \|last1=Scovil \|first1=H. E. D. \|last2=Schulz-DuBois \|first2=E. O. \|title=Three-Level Masers as Heat Engines \|journal=Physical Review Letters \|volume=2 \|issue=6 \|year=1959 \|pages=262–263 \|issn=0031-9007 \|doi=10.1103/PhysRevLett.2.262 \|bibcode=1959PhRvL...2..262S}}</ref> Geusic, Schulz-DuBois, De Grasse, and Scovil proposed quantum refrigerators, which pump heat from a cold to a hot reservoir using power, in the same year.<ref name="GeusicBois1959">{{cite journal \|last1=Geusic \|first1=J. E. \|last2=Bois \|first2=E. O. Schulz-Du \|last3=De Grasse \|first3=R. W. \|last4=Scovil \|first4=H. E. D. \|title=Three Level Spin Refrigeration and Maser Action at 1500 mc/sec \|journal=Journal of Applied Physics \|volume=30 \|issue=7 \|year=1959 \|pages=1113–1114 \|issn=0021-8979 \|doi=10.1063/1.1776991 \|bibcode=1959JAp....30.1113G}}</ref> Wineland and Hänsch suggested laser-driven processes, termed optical pumping or laser cooling.<ref name="wineland">{{cite journal \|author1=D. J. Wineland \|author2=H. Dehmelt \|title=Proposed 10<sup>14</sup>Δν < ν Laser Fluorescence Spectroscopy on Tl<sup>+</sup> Mono-Ion Oscillator III \|journal=Bull. Am. Phys. Soc. \|volume=20 \|page=637 \|year=1975 \|url=https://tf.nist.gov/general/pdf/2208.pdf}}</ref><ref name="HänschSchawlow1975">{{cite journal \|last1=Hänsch \|first1=T. W. \|last2=Schawlow \|first2=A. L. \|title=Cooling of gases by laser radiation \|journal=Optics Communications \|volume=13 \|issue=1 \|year=1975 \|pages=68–69 \|issn=0030-4018 \|doi=10.1016/0030-4018(75)90159-5 \|doi-access=free \|bibcode=1975OptCo..13...68H}}</ref><ref name="LetokhovMinogin1976">{{cite journal \|last1=Letokhov \|first1=V. S. \|last2=Minogin \|first2=V. G. \|last3=Pavlik \|first3=B. D. \|title=Cooling and trapping of atoms and molecules by a resonant laser field \|journal=Optics Communications \|volume=19 \|issue=1 \|year=1976 \|pages=72–75 \|issn=0030-4018 \|doi=10.1016/0030-4018(76)90388-6 \|bibcode=1976OptCo..19...72L}}</ref> Alicki reported that heat engines and refrigerators can function at the single-particle scale, necessitating [[Physics:Quantum thermodynamics\|quantum thermodynamics]].<ref name="alicki1">{{cite journal \|last1=Alicki \|first1=R. \|title=The quantum open system as a model of the heat engine \|journal=Journal of Physics A: Mathematical and General \|volume=12 \|issue=5 \|year=1979 \|pages=L103–L107 \|issn=0305-4470 \|doi=10.1088/0305-4470/12/5/007 \|bibcode=1979JPhA...12L.103A}}</ref>
	== 3-level amplifier ==		== 3-level amplifier ==
	[[File:Three-level-amp.pdf\|thumb\|Three-level amplifier: Levels 1 and 3 couple to the hot reservoir, levels 1 and 2 to the cold reservoir. Power results from population inversion between levels 3 and 2.]] A 3-level amplifier uses hot and cold reservoirs to maintain population inversion between two energy levels, amplifying light via stimulated emission.<ref>Yariv, Amnon (1989). ''Quantum Electronics'', 3rd ed., Wiley. {{ISBN\|0-471-60997-8}}.</ref> The ground level (1-g) and excited level (3-h) connect to a hot reservoir at temperature <math>T_\text{h}</math>, with an energy gap <math>\hbar \omega_\text{h} = E_3 - E_1</math>. At equilibrium, the population ratio is: <math display="block"> \frac{N_\text{h}}{N_\text{g}} = e^{-\frac{\hbar \omega_\text{h}}{k_\text{B} T_\text{h}}}, </math> where <math>\hbar = \frac{h}{2\pi}</math> is the Planck constant, and <math>k_\text{B}</math> is the Boltzmann constant. A cold reservoir at temperature <math>T_\text{c}</math> couples the ground level (1-g) to an intermediate level (2-c), with an energy gap <math>E_2 - E_1 = \hbar \omega_\text{c}</math>. At equilibrium: <math display="block"> \frac{N_\text{c}}{N_\text{g}} = e^{-\frac{\hbar \omega_\text{c}}{k_\text{B} T_\text{c}}}. </math> The device amplifies when levels 3-h and 2-c couple to an external field of frequency <math>\nu = \omega_\text{h} - \omega_\text{c}</math>. Efficiency, defined as the ratio of work output to heat input, is: <math display="block"> \eta = \frac{\hbar \nu}{\hbar \omega_\text{h}} = 1 - \frac{\omega_\text{c}}{\omega_\text{h}}. </math> Amplification requires population inversion: <math display="block"> G = N_\text{h} - N_\text{c} \ge 0, </math> equivalent to: <math display="block"> \frac{\hbar \omega_\text{c}}{k_\text{B} T_\text{c}} \ge \frac{\hbar \omega_\text{h}}{k_\text{B} T_\text{h}}. </math> This leads to an efficiency limit: <math display="block"> \eta \le 1 - \frac{T_\text{c}}{T_\text{h}} = \eta_\text{c}, </math> where <math>\eta_\text{c}</math> is the Carnot cycle efficiency, achieved at zero gain (<math>G = 0</math>). Reversing the process creates a refrigerator, with a coefficient of performance (COP): <math display="block"> \epsilon = \frac{\omega_\text{c}}{\nu} \le \frac{T_\text{c}}{T_\text{h} - T_\text{c}}. </math>		A 3-level amplifier uses hot and cold reservoirs to maintain population inversion between two energy levels, amplifying light via stimulated emission.<ref>Yariv, Amnon (1989). ''Quantum Electronics'', 3rd ed., Wiley. {{ISBN\|0-471-60997-8}}.</ref> The ground level (1-g) and excited level (3-h) connect to a hot reservoir at temperature <math>T_\text{h}</math>, with an energy gap <math>\hbar \omega_\text{h} = E_3 - E_1</math>. At equilibrium, the population ratio is: <math display="block"> \frac{N_\text{h}}{N_\text{g}} = e^{-\frac{\hbar \omega_\text{h}}{k_\text{B} T_\text{h}}}, </math> where <math>\hbar = \frac{h}{2\pi}</math> is the Planck constant, and <math>k_\text{B}</math> is the Boltzmann constant. A cold reservoir at temperature <math>T_\text{c}</math> couples the ground level (1-g) to an intermediate level (2-c), with an energy gap <math>E_2 - E_1 = \hbar \omega_\text{c}</math>. At equilibrium: <math display="block"> \frac{N_\text{c}}{N_\text{g}} = e^{-\frac{\hbar \omega_\text{c}}{k_\text{B} T_\text{c}}}. </math> The device amplifies when levels 3-h and 2-c couple to an external field of frequency <math>\nu = \omega_\text{h} - \omega_\text{c}</math>. Efficiency, defined as the ratio of work output to heat input, is: <math display="block"> \eta = \frac{\hbar \nu}{\hbar \omega_\text{h}} = 1 - \frac{\omega_\text{c}}{\omega_\text{h}}. </math> Amplification requires population inversion: <math display="block"> G = N_\text{h} - N_\text{c} \ge 0, </math> equivalent to: <math display="block"> \frac{\hbar \omega_\text{c}}{k_\text{B} T_\text{c}} \ge \frac{\hbar \omega_\text{h}}{k_\text{B} T_\text{h}}. </math> This leads to an efficiency limit: <math display="block"> \eta \le 1 - \frac{T_\text{c}}{T_\text{h}} = \eta_\text{c}, </math> where <math>\eta_\text{c}</math> is the Carnot cycle efficiency, achieved at zero gain (<math>G = 0</math>). Reversing the process creates a refrigerator, with a coefficient of performance (COP): <math display="block"> \epsilon = \frac{\omega_\text{c}}{\nu} \le \frac{T_\text{c}}{T_\text{h} - T_\text{c}}. </math>
	== Types ==		== Types ==
	Quantum devices operate either continuously or via reciprocating cycles. Continuous devices include solar cells, thermoelectric devices (outputting current), and lasers (outputting coherent light). Continuous refrigerators use optical pumping or laser cooling.<ref name="NareviciusBannerman2009">{{cite journal\|last1=Narevicius\|first1=Edvardas\|last2=Bannerman\|first2=S Travis\|last3=Raizen\|first3=Mark G\|title=Single-photon molecular cooling\|journal=New Journal of Physics\|volume=11\|issue=5\|year=2009\|article-number=055046\|issn=1367-2630\|doi=10.1088/1367-2630/11/5/055046\|doi-access=free\|bibcode=2009NJPh...11e5046N\|arxiv=0808.1383}}</ref><ref name="am1">{{cite journal\|last1=Kosloff\|first1=Ronnie\|last2=Levy\|first2=Amikam\|title=Quantum Heat Engines and Refrigerators: Continuous Devices\|journal=Annual Review of Physical Chemistry\|volume=65\|issue=1\|year=2014\|pages=365–393\|issn=0066-426X\|doi=10.1146/annurev-physchem-040513-103724\|pmid=24689798\|arxiv=1310.0683\|bibcode=2014ARPC...65..365K\|s2cid=25266545}}</ref> Reciprocating devices, such as four-stroke or two-stroke machines, mimic classical engines with non-commuting strokes. Common cycles include the Carnot cycle<ref name="geva2">{{cite journal\|last1=Geva\|first1=Eitan\|last2=Kosloff\|first2=Ronnie\|title=A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid\|journal=The Journal of Chemical Physics\|volume=96\|issue=4\|year=1992\|pages=3054–3067\|issn=0021-9606\|doi=10.1063/1.461951\|bibcode=1992JChPh..96.3054G}}</ref><ref name="bender">{{cite journal\|last1=Bender\|first1=Carl M\|last2=Brody\|first2=Dorje C\|last3=Meister\|first3=Bernhard K\|title=Quantum mechanical Carnot engine\|journal=Journal of Physics A: Mathematical and General\|volume=33\|issue=24\|year=2000\|pages=4427–4436\|issn=0305-4470\|doi=10.1088/0305-4470/33/24/302\|arxiv=quant-ph/0007002\|bibcode=2000JPhA...33.4427B\|s2cid=5335}}</ref> and Otto cycle.<ref name="tova">{{cite journal\|last1=Feldmann\|first1=Tova\|last2=Kosloff\|first2=Ronnie\|title=Performance of discrete heat engines and heat pumps in finite time\|journal=Physical Review E\|volume=61\|issue=5\|year=2000\|pages=4774–4790\|issn=1063-651X\|doi=10.1103/PhysRevE.61.4774\|pmid=11031518\|bibcode=2000PhRvE..61.4774F\|arxiv=physics/0003007\|s2cid=2277942}}</ref> These cycles yield equations of motion for the working medium and heat flux.		Quantum devices operate either continuously or via reciprocating cycles. Continuous devices include solar cells, thermoelectric devices (outputting current), and lasers (outputting coherent light). Continuous refrigerators use optical pumping or laser cooling.<ref name="NareviciusBannerman2009">{{cite journal\|last1=Narevicius\|first1=Edvardas\|last2=Bannerman\|first2=S Travis\|last3=Raizen\|first3=Mark G\|title=Single-photon molecular cooling\|journal=New Journal of Physics\|volume=11\|issue=5\|year=2009\|article-number=055046\|issn=1367-2630\|doi=10.1088/1367-2630/11/5/055046\|doi-access=free\|bibcode=2009NJPh...11e5046N\|arxiv=0808.1383}}</ref><ref name="am1">{{cite journal\|last1=Kosloff\|first1=Ronnie\|last2=Levy\|first2=Amikam\|title=Quantum Heat Engines and Refrigerators: Continuous Devices\|journal=Annual Review of Physical Chemistry\|volume=65\|issue=1\|year=2014\|pages=365–393\|issn=0066-426X\|doi=10.1146/annurev-physchem-040513-103724\|pmid=24689798\|arxiv=1310.0683\|bibcode=2014ARPC...65..365K\|s2cid=25266545}}</ref> Reciprocating devices, such as four-stroke or two-stroke machines, mimic classical engines with non-commuting strokes. Common cycles include the Carnot cycle<ref name="geva2">{{cite journal\|last1=Geva\|first1=Eitan\|last2=Kosloff\|first2=Ronnie\|title=A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid\|journal=The Journal of Chemical Physics\|volume=96\|issue=4\|year=1992\|pages=3054–3067\|issn=0021-9606\|doi=10.1063/1.461951\|bibcode=1992JChPh..96.3054G}}</ref><ref name="bender">{{cite journal\|last1=Bender\|first1=Carl M\|last2=Brody\|first2=Dorje C\|last3=Meister\|first3=Bernhard K\|title=Quantum mechanical Carnot engine\|journal=Journal of Physics A: Mathematical and General\|volume=33\|issue=24\|year=2000\|pages=4427–4436\|issn=0305-4470\|doi=10.1088/0305-4470/33/24/302\|arxiv=quant-ph/0007002\|bibcode=2000JPhA...33.4427B\|s2cid=5335}}</ref> and Otto cycle.<ref name="tova">{{cite journal\|last1=Feldmann\|first1=Tova\|last2=Kosloff\|first2=Ronnie\|title=Performance of discrete heat engines and heat pumps in finite time\|journal=Physical Review E\|volume=61\|issue=5\|year=2000\|pages=4774–4790\|issn=1063-651X\|doi=10.1103/PhysRevE.61.4774\|pmid=11031518\|bibcode=2000PhRvE..61.4774F\|arxiv=physics/0003007\|s2cid=2277942}}</ref> These cycles yield equations of motion for the working medium and heat flux.
	=== Reciprocating ===		=== Reciprocating ===
	~~{{see also\|Reciprocating heat engine}}~~ Researchers studied quantum versions of thermodynamic cycles, including the Carnot cycle,<ref name="geva2" /><ref name="bender" /><ref name="QuanLiu2007">{{cite journal\|last1=Quan\|first1=H. T.\|last2=Liu\|first2=Yu-xi\|last3=Sun\|first3=C. P.\|last4=Nori\|first4=Franco\|title=Quantum thermodynamic cycles and quantum heat engines\|journal=Physical Review E\|volume=76\|issue=3\|article-number=031105\|year=2007\|issn=1539-3755\|doi=10.1103/PhysRevE.76.031105\|pmid=17930197\|bibcode=2007PhRvE..76c1105Q\|arxiv=quant-ph/0611275\|s2cid=3009953}}</ref> Stirling cycle,<ref name="WuChen1998">{{cite journal\|last1=Wu\|first1=F.\|last2=Chen\|first2=L.\|last3=Sun\|first3=F.\|last4=Wu\|first4=C.\|last5=Zhu\|first5=Yonghong\|title=Performance and optimization criteria for forward and reverse quantum Stirling cycles\|journal=Energy Conversion and Management\|volume=39\|issue=8\|year=1998\|pages=733–739\|issn=0196-8904\|doi=10.1016/S0196-8904(97)10037-1\|bibcode=1998ECM....39..733W }}</ref> and Otto cycle.<ref name="tova" /><ref name="Kieu2006">{{cite journal\|last1=Kieu\|first1=T. D.\|title=Quantum heat engines, the second law and Maxwell's daemon\|journal=The European Physical Journal D\|volume=39\|issue=1\|year=2006\|pages=115–128\|issn=1434-6060\|doi=10.1140/epjd/e2006-00075-5\|bibcode=2006EPJD...39..115K\|arxiv=quant-ph/0311157\|s2cid=119382163}}</ref> The Otto cycle serves as a model for other reciprocating cycles. [[File:Q-otto-cycle.pdf\|thumb\|Quantum Otto cycle in the Entropy <math>\Omega</math> plane, showing energy entropy and [[Physics:Von Neumann entropy\|Von Neumann entropy]]. <math>\Omega</math> represents the externally controlled internal frequency, mimicking inverse volume in the Otto cycle. Red and blue lines indicate hot and cold isochores. The cycle represents a heat pump.]] The Otto cycle consists of four segments:		Researchers studied quantum versions of thermodynamic cycles, including the Carnot cycle,<ref name="geva2" /><ref name="bender" /><ref name="QuanLiu2007">{{cite journal\|last1=Quan\|first1=H. T.\|last2=Liu\|first2=Yu-xi\|last3=Sun\|first3=C. P.\|last4=Nori\|first4=Franco\|title=Quantum thermodynamic cycles and quantum heat engines\|journal=Physical Review E\|volume=76\|issue=3\|article-number=031105\|year=2007\|issn=1539-3755\|doi=10.1103/PhysRevE.76.031105\|pmid=17930197\|bibcode=2007PhRvE..76c1105Q\|arxiv=quant-ph/0611275\|s2cid=3009953}}</ref> Stirling cycle,<ref name="WuChen1998">{{cite journal\|last1=Wu\|first1=F.\|last2=Chen\|first2=L.\|last3=Sun\|first3=F.\|last4=Wu\|first4=C.\|last5=Zhu\|first5=Yonghong\|title=Performance and optimization criteria for forward and reverse quantum Stirling cycles\|journal=Energy Conversion and Management\|volume=39\|issue=8\|year=1998\|pages=733–739\|issn=0196-8904\|doi=10.1016/S0196-8904(97)10037-1\|bibcode=1998ECM....39..733W }}</ref> and Otto cycle.<ref name="tova" /><ref name="Kieu2006">{{cite journal\|last1=Kieu\|first1=T. D.\|title=Quantum heat engines, the second law and Maxwell's daemon\|journal=The European Physical Journal D\|volume=39\|issue=1\|year=2006\|pages=115–128\|issn=1434-6060\|doi=10.1140/epjd/e2006-00075-5\|bibcode=2006EPJD...39..115K\|arxiv=quant-ph/0311157\|s2cid=119382163}}</ref> The Otto cycle serves as a model for other reciprocating cycles. [[File:Q-otto-cycle.pdf\|thumb\|Quantum Otto cycle in the Entropy <math>\Omega</math> plane, showing energy entropy and [[Physics:Von Neumann entropy\|Von Neumann entropy]]. <math>\Omega</math> represents the externally controlled internal frequency, mimicking inverse volume in the Otto cycle. Red and blue lines indicate hot and cold isochores. The cycle represents a heat pump.]] The Otto cycle consists of four segments:
	* Segment <math>A \rightarrow B</math>: Isomagnetic or isochoric process, partial equilibration with the cold reservoir, described by propagator <math>U_\text{c}</math>.		* Segment <math>A \rightarrow B</math>: Isomagnetic or isochoric process, partial equilibration with the cold reservoir, described by propagator <math>U_\text{c}</math>.
	* Segment <math>B \rightarrow C</math>: Magnetization or adiabatic compression, expanding energy level gaps in the Hamiltonian, described by propagator <math>U_\text{ch}</math>.		* Segment <math>B \rightarrow C</math>: Magnetization or adiabatic compression, expanding energy level gaps in the Hamiltonian, described by propagator <math>U_\text{ch}</math>.
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	<!--- Categories --->		<!--- Categories --->
	~~[[Category:Quantum mechanics]]~~
	~~[[Category:Heat pumps]]~~
	~~[[Category:Thermodynamics]]~~

	{{Sourceattribution\|Quantum heat engines\|1}}		{{Sourceattribution\|Quantum heat engines\|1}}

WikiHarold: Clean Quantum page image and red links

2026-05-23T23:34:37Z

Clean Quantum page image and red links

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WikiHarold: Expand short Quantum intro

2026-05-23T22:58:41Z

Expand short Quantum intro

← Older revision		Revision as of 22:58, 23 May 2026
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	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	~~{{Infobox technology \| name =~~ Quantum heat ~~engine \| image = \| caption = \| inventor = \| invention_date = 1959 \| type = Heat engine \| operating_principle =~~ Quantum ~~mechanics \| applications = Power generation, refrigeration }}~~		Quantum heat engines are a Book I topic in the Quantum Collection. A quantum heat engine converts heat flow into useful work when the working medium must be described by quantum mechanics. Its active system may be a few-level atom, a spin, a harmonic oscillator, a qubit, or another microscopic device coupled to hot and cold reservoirs. Quantum versions of amplifier, Otto, Carnot, and absorption cycles show how coherence, discreteness, measurement, and open-system dynamics affect thermodynamic performance. The topic connects quantum thermodynamics, heat transport, refrigerators, finite-time cycles, and the limits imposed by the second and third laws.
	A ~~'''~~quantum heat engine~~''' generates power from~~ heat flow ~~between~~ hot and cold reservoirs, ~~operating under~~ the ~~principles of [[Physics:Quantum mechanics\|quantum mechanics]]~~.
	</div>		</div>

Harold: Add missing image fallback to Quantum header

2026-05-17T22:33:15Z

Add missing image fallback to Quantum header

← Older revision		Revision as of 22:33, 17 May 2026
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	~~<!--~~ No ~~lead~~ image available ~~in existing page~~. ~~-->~~		[[File:File not found.png\|thumb\|280px\|No image available.]]
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Harold: Restore Quantum article header template

2026-05-17T21:52:39Z

Restore Quantum article header template

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 {{Infobox technology | name = Quantum heat engine | image = | caption = | inventor = | invention_date = 1959 | type = Heat engine | operating_principle = Quantum mechanics | applications = Power generation, refrigeration }}
 A '''quantum heat engine''' generates power from heat flow between hot and cold reservoirs, operating under the principles of [[Physics:Quantum mechanics|quantum mechanics]].
 == History ==

imported>WikiHarold: attribution_corrected

2026-02-26T22:49:34Z

attribution_corrected

← Older revision	Revision as of 22:49, 26 February 2026
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imported>WikiHarold: attribution_corrected

2026-02-26T22:49:34Z

attribution_corrected

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