Quantum Thermodynamics: A Dynamical Viewpoint

Quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. The viewpoint advocated is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The emergence of the 0-law, I-law, II-law and III-law of thermodynamics from quantum considerations is presented. The emphasis is on consistency between the two theories, which address the same subject from different foundations. We claim that inconsistency is the result of faulty analysis, pointing to flaws in approximations.

[1]  A. Einstein Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt [AdP 17, 132 (1905)] , 2005, Annalen der Physik.

[2]  Sadi Carnot,et al.  Réflexions Sur La Puissance Motrice Du Feu Et Sur Les Machines Propres À Développer Cette Puissance , 2015 .

[3]  M. Büttiker,et al.  Magnon-driven quantum-dot heat engine , 2012, 1206.1259.

[4]  J. G. Muga,et al.  Shortcut to adiabatic passage in two- and three-level atoms. , 2010, Physical review letters.

[5]  A. Allahverdyan,et al.  Work extremum principle: structure and function of quantum heat engines. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  R. Kubo Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems , 1957 .

[7]  R. Clausius,et al.  Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen , 1850 .

[8]  Herbert Spohn,et al.  Irreversible Thermodynamics for Quantum Systems Weakly Coupled to Thermal Reservoirs , 2007 .

[9]  I. Tsujikawa,et al.  Possibility of Optical Cooling of Ruby , 1963 .

[10]  S Zienau Optical Resonance and Two Level Atoms , 1975 .

[11]  W. W. Hansen,et al.  Nuclear Induction , 2011 .

[12]  J. Teufel,et al.  Sideband cooling of micromechanical motion to the quantum ground state , 2011, Nature.

[13]  MAXWELL’S DEMONS,et al.  Quantum Discord and Maxwell's Demons , 2002 .

[14]  Claudio Chamon,et al.  Cooling through optimal control of quantum evolution , 2013 .

[15]  Jincan Chen,et al.  The performance evaluation of a micro/nano-scaled cooler working with an ideal Bose gas , 2012 .

[16]  M. Partovi Irreversibility, reduction, and entropy increase in quantum measurements , 1989 .

[17]  Marlan O Scully,et al.  Quantum photocell: using quantum coherence to reduce radiative recombination and increase efficiency. , 2010, Physical review letters.

[18]  J. E. Geusic,et al.  Three Level Spin Refrigeration and Maser Action at 1500 mc/sec , 1959 .

[19]  Ronnie Kosloff,et al.  Irreversible performance of a quantum harmonic heat engine , 2006 .

[20]  Peter Salamon,et al.  Heat engines in finite time governed by master equations , 1996 .

[21]  Pérès,et al.  Distribution of matrix elements of chaotic systems. , 1986, Physical review. A, General physics.

[22]  A. Frigerio Quantum dynamical semigroups and approach to equilibrium , 1977 .

[23]  Massimiliano Esposito,et al.  Efficiency at maximum power of low-dissipation Carnot engines. , 2010, Physical review letters.

[24]  R. Kosloff,et al.  Rise and fall of quantum and classical correlations in open-system dynamics , 2006, quant-ph/0605140.

[25]  G. Lindblad On the existence of quantum subdynamics , 1996 .

[26]  K. Kraus General state changes in quantum theory , 1971 .

[27]  Robert Alicki,et al.  The quantum open system as a model of the heat engine , 1979 .

[28]  Heinz Schättler,et al.  Time-optimal frictionless atom cooling in harmonic traps , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[29]  G. Lindblad On the generators of quantum dynamical semigroups , 1976 .

[30]  R. Kosloff,et al.  Algorithm for simulation of quantum many-body dynamics using dynamical coarse-graining , 2008, 0812.3143.

[31]  Julian Schwinger,et al.  Theory of Many-Particle Systems. I , 1959 .

[32]  F. Rempp,et al.  Quantum thermodynamic Otto machines: A spin-system approach , 2007 .

[33]  G. Thomas,et al.  Coupled quantum Otto cycle. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Ronnie Kosloff,et al.  Quantum four-stroke heat engine: thermodynamic observables in a model with intrinsic friction. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  L. Bruneau,et al.  Landauer-Büttiker Formula and Schrödinger Conjecture , 2012, 1201.3190.

[36]  J. G. Muga,et al.  Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity. , 2009, Physical review letters.

[37]  Robert S. Whitney,et al.  Thermodynamic and quantum bounds on nonlinear DC thermoelectric transport , 2012, 1211.4737.

[38]  I. Ventura Theory of Superfluidity , 1979 .

[39]  W. Nernst Die theoretischen und experimentellen Grundlagen des neuen Wärmesatzes , 1918 .

[40]  Entropy exchange and entanglement in the Jaynes-Cummings model (7 pages) , 2005, quant-ph/0505119.

[41]  Normal-metal-superconductor tunnel junction as a Brownian refrigerator. , 2007, Physical review letters.

[42]  Tien D Kieu The second law, Maxwell's demon, and work derivable from quantum heat engines. , 2004, Physical review letters.

[43]  R. Harney,et al.  Optical resonance and two-level atoms , 1978, IEEE Journal of Quantum Electronics.

[44]  Nieuwenhuizen,et al.  Extraction of work from a single thermal bath in the quantum regime , 2000, Physical review letters.

[45]  T. Hänsch,et al.  Cooling of gases by laser radiation , 1975 .

[46]  M. Raizen,et al.  Single-photon cooling at the limit of trap dynamics: Maxwell's demon near maximum efficiency , 2008, 0810.2239.

[47]  Srednicki Chaos and quantum thermalization. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[48]  A. Polkovnikov Microscopic diagonal entropy and its connection to basic thermodynamic relations , 2008, 0806.2862.

[49]  Xian He,et al.  The performance characteristics of an irreversible quantum Otto harmonic refrigeration cycle , 2009 .

[50]  Ronnie Kosloff,et al.  Optimal performance of reciprocating demagnetization quantum refrigerators. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  L. Brillouin,et al.  Science and information theory , 1956 .

[52]  G. Kurizki,et al.  Minimal universal quantum heat machine. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  G. Lindblad Expectations and entropy inequalities for finite quantum systems , 1974 .

[54]  Lukas Novotny,et al.  Subkelvin parametric feedback cooling of a laser-trapped nanoparticle. , 2012, Physical review letters.

[55]  K. Lendi,et al.  Quantum Dynamical Semigroups and Applications , 1987 .

[56]  Ronnie Kosloff,et al.  Discrete four-stroke quantum heat engine exploring the origin of friction. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  A. Frigerio,et al.  Stationary states of quantum dynamical semigroups , 1978 .

[58]  Shor,et al.  Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[59]  Jeffrey M. Gordon,et al.  Quantum refrigerators in quest of the absolute zero , 2000 .

[60]  R. The Low Density Limit for an N-Level System Interacting with a Free Bose or Fermi Gas , 2022 .

[61]  E. Boukobza D. J. Tannor Thermodynamic analysis of quantum light amplification , 2006 .

[62]  L. Szilard über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen , 1929 .

[63]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[64]  Franco Nori,et al.  Quantum thermodynamic cycles and quantum heat engines. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[65]  M. Rigol,et al.  Thermalization and its mechanism for generic isolated quantum systems , 2007, Nature.

[66]  C. Regal,et al.  Cooling a Single Atom in an Optical Tweezer to Its Quantum Ground State , 2012, 1209.2087.

[67]  R. Kosloff,et al.  On the relaxation of a two-level system driven by a strong electromagnetic field , 1995 .

[68]  P. Landsberg Foundations of Thermodynamics , 1956 .

[69]  R. K. Wangsness,et al.  The Dynamical Theory of Nuclear Induction , 1953 .

[70]  Time-optimal processes for interacting spin systems , 2012 .

[71]  On the nature of thermodynamic extremum principles: The case of maximum efficiency and maximum work , 2008 .

[72]  Lajos Diósi,et al.  Non-markovian continuous quantum measurement of retarded observables. , 2008, Physical review letters.

[73]  F. Curzon,et al.  Efficiency of a Carnot engine at maximum power output , 1975 .

[74]  E. Davies,et al.  Markovian master equations , 1974 .

[75]  H. Wang Quantum-mechanical Brayton engine working with a particle in a one-dimensional harmonic trap , 2013 .

[76]  M. Scully,et al.  Enhancing photovoltaic power by Fano-induced coherence , 2011 .

[77]  Bernhard K. Meister,et al.  Entropy and temperature of a quantum Carnot engine , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[78]  E. O. Schulz-DuBois,et al.  Three-Level Masers as Heat Engines , 1959 .

[79]  J. Paz,et al.  Dynamics and thermodynamics of linear quantum open systems. , 2012, Physical review letters.

[80]  Robert Alicki,et al.  Markovian master equation and thermodynamics of a two-level system in a strong laser field. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[81]  Ronnie Kosloff,et al.  Quantum absorption refrigerator. , 2011, Physical review letters.

[82]  I. I. Ivanchik THEORY OF THE MANY-PARTICLE SYSTEMS. , 1968 .

[83]  Hao Wang,et al.  Thermal entanglement in two-atom cavity QED and the entangled quantum Otto engine. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[84]  E. Davies A model of atomic radiation , 1978 .

[85]  D. A. Edwards The mathematical foundations of quantum mechanics , 1979, Synthese.

[86]  Deutsch,et al.  Quantum statistical mechanics in a closed system. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[87]  Paul Skrzypczyk,et al.  How small can thermal machines be? The smallest possible refrigerator. , 2009, Physical review letters.

[88]  Ronnie Kosloff,et al.  On the classical limit of quantum thermodynamics in finite time , 1992 .

[89]  Karl Heinz Hoffmann,et al.  Time-optimal controls for frictionless cooling in harmonic traps , 2011 .

[90]  Cyclic cooling algorithm , 2007, quant-ph/0702071.

[91]  P. Salamon,et al.  Principles of control thermodynamics , 2001 .

[92]  Thomas Jahnke,et al.  Quantum thermodynamic processes: a control theory for machine cycles , 2007, 0712.0534.

[93]  E Torrontegui,et al.  Multiple Schrödinger pictures and dynamics in shortcuts to adiabaticity. , 2011, Physical review letters.

[94]  Ronnie Kosloff,et al.  Quantum lubrication: suppression of friction in a first-principles four-stroke heat engine. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[95]  J M Gordon,et al.  Quantum thermodynamic cooling cycle. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[96]  Bjarne Andresen,et al.  Thermodynamics in finite time , 1984 .

[97]  Ronnie Kosloff,et al.  A quantum mechanical open system as a model of a heat engine , 1984 .

[98]  F. Belgiorno Notes on the Third Law of Thermodynamics.I , 2002 .

[99]  P. Landsberg A comment on Nernst's theorem , 1989 .

[100]  W. Nernst Ueber die Berechnung chemischer Gleichgewichte aus thermischen Messungen , 1906 .

[101]  Physics Letters , 1962, Nature.

[102]  Jincan Chen,et al.  The performance analysis of a micro-/nanoscaled quantum heat engine , 2012 .

[103]  E. Lieb,et al.  The physics and mathematics of the second law of thermodynamics (Physics Reports 310 (1999) 1–96)☆ , 1997, cond-mat/9708200.

[104]  G. Kurizki,et al.  Quantum bath refrigeration towards absolute zero: challenging the unattainability principle. , 2012, Physical review letters.

[105]  R. Kosloff,et al.  Short time cycles of purely quantum refrigerators. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[106]  W. Lamb Theory of an optical maser , 1964 .

[107]  The low density limit for anN-level system interacting with a free bose or fermi gas , 1985 .

[108]  J. E. Geusic,et al.  Quantum Equivalent of the Carnot Cycle , 1967 .

[109]  J. Rossnagel,et al.  Single-ion heat engine at maximum power. , 2012, Physical review letters.

[110]  R. Kosloff,et al.  Characteristics of the limit cycle of a reciprocating quantum heat engine. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[111]  ON THE EXACT IDENTITY BETWEEN THERMODYNAMIC AND INFORMATIC ENTROPIES IN A UNITARY MODEL OF FRICTION , 2005, quant-ph/0505219.

[112]  Seth Lloyd,et al.  Quantum-mechanical Maxwell’s demon , 1997 .

[113]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[114]  Feldmann,et al.  Performance of discrete heat engines and heat pumps in finite time , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[115]  Ronnie Kosloff,et al.  The quantum heat engine and heat pump: An irreversible thermodynamic analysis of the three-level amplifier , 1996 .

[116]  Gérard G. Emch,et al.  Algebraic methods in statistical mechanics and quantum field theory , 1972 .

[117]  R. Kosloff,et al.  Efficient simulation of quantum evolution using dynamical coarse graining , 2008, 0803.3267.

[118]  Jincan Chen,et al.  Quantum refrigeration cycles using spin-1/2 systems as the working substance. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[119]  N. Bogolyubov On the theory of superfluidity , 1947 .

[120]  Karl Heinz Hoffmann,et al.  Maximum work in minimum time from a conservative quantum system. , 2009, Physical chemistry chemical physics : PCCP.

[121]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[122]  Wojciech Hubert Zurek Quantum discord and Maxwell's demons , 2003 .

[123]  L. Di'osi,et al.  Continuous quantum measurement and itô formalism , 1988, 1812.11591.

[124]  Efficiency at maximum power of a heat engine working with a two-level atomic system. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[125]  C. Van den Broeck,et al.  Cooling by heating: refrigeration powered by photons. , 2012, Physical review letters.

[126]  B. Andresen,et al.  Minimum entropy production and the optimization of heat engines , 1980 .

[127]  H. Ritsch,et al.  Temperature gradient driven lasing and stimulated cooling. , 2012, Physical review letters.

[128]  Jizhou He,et al.  Thermal entangled four-level quantum Otto heat engine , 2012 .

[129]  Zhen-Xiang Gong,et al.  Entropy Generation Minimization , 1996 .

[130]  Bernhard H. Haak,et al.  Open Quantum Systems , 2019, Tutorials, Schools, and Workshops in the Mathematical Sciences.

[131]  Franco Nori,et al.  Colloquium: The physics of Maxwell's demon and information , 2007, 0707.3400.

[132]  Marlan O Scully,et al.  Extracting work from a single heat bath via vanishing quantum coherence. , 2002, Science.

[133]  Ronnie Kosloff,et al.  Quantum refrigerators and the third law of thermodynamics. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[134]  Karl Heinz Hoffmann,et al.  The quantum refrigerator: The quest for absolute zero , 2008, 0808.0229.

[135]  Ronnie Kosloff,et al.  A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid , 1992 .

[136]  D. Comparat,et al.  General conditions for quantum adiabatic evolution , 2006, 0906.4453.

[137]  S. Deléglise,et al.  Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode , 2011, Nature.

[138]  T. Feldmann,et al.  Minimal temperature of quantum refrigerators , 2009, 0902.0326.

[139]  A. Nitzan,et al.  Molecular heat pump. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[140]  L. Diósi A Short Course in Quantum Information Theory: An Approach From Theoretical Physics , 2006 .

[141]  Massimiliano Esposito,et al.  Thermoelectric efficiency at maximum power in a quantum dot , 2008, 0808.0216.

[142]  D. Segal Vibrational relaxation in the Kubo oscillator: stochastic pumping of heat. , 2009, The Journal of chemical physics.

[143]  R. Kosloff,et al.  Beyond linear response: Line shapes for coupled spins or oscillators via direct calculation of dissipated power , 1984 .

[144]  Christoph Becher,et al.  Feedback cooling of a single trapped ion. , 2006, Physical review letters.

[145]  G. Kurizki,et al.  Quantum bath refrigeration towards absolute zero: unattainability principle challenged , 2012, 1208.1015.