Resource theory of quantum thermodynamics: Thermal operations and Second Laws

Resource theories are a generic approach used to manage any valuable resource, such as entanglement, purity, and asymmetry. Such frameworks are characterized by two main elements: a set of predefined (free) operations and states, that one assumes to be easily obtained at no cost. Given these ground rules, one can ask: what is achievable by using such free operations and states? This usually results in a set of state transition conditions, that tell us if a particular state $ \rho $ may evolve into another state $ \rho' $ via the usage of free operations and states. We shall see in this chapter that thermal interactions can be modelled as a resource theory. The state transition conditions arising out of such a framework, are then referred to as "second laws". We shall also see how such state transition conditions recover classical thermodynamics in the i.i.d. limit. Finally, we discuss how these laws are applied to study fundamental limitations to the performance of quantum heat engines.

[1]  Ian T. Durham,et al.  Information and Interaction , 2017 .

[2]  Michal Horodecki,et al.  The second laws of quantum thermodynamics , 2013, Proceedings of the National Academy of Sciences.

[3]  Andreas J. Winter,et al.  A Resource Framework for Quantum Shannon Theory , 2008, IEEE Transactions on Information Theory.

[4]  Nicole Yunger Halpern,et al.  The resource theory of informational nonequilibrium in thermodynamics , 2013, 1309.6586.

[6]  M. Horodecki,et al.  Fundamental limitations for quantum and nanoscale thermodynamics , 2011, Nature Communications.

[7]  R. Duan,et al.  Quantum majorization and a complete set of entropic conditions for quantum thermodynamics , 2017, Nature Communications.

[8]  R. Spekkens,et al.  The resource theory of quantum reference frames: manipulations and monotones , 2007, 0711.0043.

[9]  U. Seifert Stochastic thermodynamics, fluctuation theorems and molecular machines , 2012, Reports on progress in physics. Physical Society.

[10]  David Jennings,et al.  Thermodynamic resource theories, non-commutativity and maximum entropy principles , 2015, 1511.04420.

[11]  R. Renner,et al.  A measure of majorization emerging from single-shot statistical mechanics , 2012, 1207.0434.

[12]  'Alvaro M. Alhambra,et al.  Elementary Thermal Operations , 2016, 1607.00394.

[13]  Andreas Winter,et al.  Quantum reference frames and their applications to thermodynamics , 2018, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  Massimiliano Esposito,et al.  Second law and Landauer principle far from equilibrium , 2011, 1104.5165.

[15]  J. Åberg Catalytic coherence. , 2013, Physical review letters.

[16]  Jonathan Oppenheim,et al.  Are the laws of entanglement theory thermodynamical? , 2002, Physical review letters.

[17]  M. Marthaler,et al.  Bidirectional single-electron counting and the fluctuation theorem , 2009, 0908.0229.

[18]  Lluis Masanes,et al.  Work extraction from quantum systems with bounded fluctuations in work , 2016, Nature communications.

[19]  C. Jarzynski Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale , 2011 .

[20]  A. J. Short,et al.  Work extraction and thermodynamics for individual quantum systems , 2013, Nature Communications.

[21]  W. Pusz,et al.  Passive states and KMS states for general quantum systems , 1978 .

[22]  F. Reif,et al.  Fundamentals of Statistical and Thermal Physics , 1965 .

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

[24]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[25]  R. Renner,et al.  Fundamental work cost of quantum processes , 2017, 1709.00506.

[26]  Nicole Yunger Halpern Toward Physical Realizations of Thermodynamic Resource Theories , 2015, 1509.03873.

[27]  A. J. Short,et al.  Thermodynamics of quantum systems with multiple conserved quantities , 2015, Nature Communications.

[28]  G. Gallavotti,et al.  Nonequilibrium thermodynamics , 2003, 1901.08821.

[29]  Karoline Wiesner,et al.  Fluctuations in single-shot ε -deterministic work extraction , 2017 .

[30]  Stephanie Wehner,et al.  Surpassing the Carnot efficiency by extracting imperfect work , 2016, 1606.05532.

[31]  Masahide Sasaki,et al.  Entanglement distillation from Gaussian input states , 2010 .

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

[33]  Stefanie Hilt,et al.  System-bath entanglement in quantum thermodynamics , 2009 .

[34]  A. Winter,et al.  Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges , 2015, Nature Communications.

[35]  Herbert Walther,et al.  Extracting Work from a Single Heat Bath via Vanishing Quantum Coherence , 2003, Science.

[36]  Jonathan Oppenheim,et al.  A Sufficient Set of Experimentally Implementable Thermal Operations for Small Systems , 2015, Physical Review X.

[37]  M. Plenio,et al.  Entanglement-Assisted Local Manipulation of Pure Quantum States , 1999, quant-ph/9905071.

[38]  Johan Aberg,et al.  The thermodynamic meaning of negative entropy , 2010, Nature.

[39]  Ronnie Kosloff,et al.  Equivalence of Quantum Heat Machines, and Quantum-Thermodynamic Signatures , 2015 .

[40]  Nicole Yunger Halpern Beyond heat baths II: framework for generalized thermodynamic resource theories , 2014, 1409.7845.

[41]  Jonathan Oppenheim,et al.  Fluctuating States: What is the Probability of a Thermodynamical Transition? , 2015, 1504.00020.

[42]  Marlan O Scully,et al.  Quantum afterburner: improving the efficiency of an ideal heat engine. , 2002, Physical review letters.

[43]  David Jennings,et al.  Description of quantum coherence in thermodynamic processes requires constraints beyond free energy , 2014, Nature Communications.

[44]  J. Rossnagel,et al.  Nanoscale heat engine beyond the Carnot limit. , 2013, Physical review letters.

[45]  Nicolas Léonard Sadi Carnot,et al.  Reflections on the Motive Power of Fire , 1824 .

[46]  J Eisert,et al.  Exact relaxation in a class of nonequilibrium quantum lattice systems. , 2008, Physical review letters.

[47]  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.

[48]  A. Winter,et al.  Operational Resource Theory of Coherence. , 2015, Physical review letters.

[49]  'Alvaro M. Alhambra,et al.  Fluctuating Work: From Quantum Thermodynamical Identities to a Second Law Equality , 2016, 1601.05799.

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

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

[52]  K. Audenaert A sharp continuity estimate for the von Neumann entropy , 2006, quant-ph/0610146.

[53]  R. Spekkens,et al.  The theory of manipulations of pure state asymmetry: I. Basic tools, equivalence classes and single copy transformations , 2011, 1104.0018.

[54]  G. Crooks Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems , 1998 .

[55]  Markus P. Mueller,et al.  Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics , 2016, 1605.06092.

[56]  T. Rudolph,et al.  Quantum coherence, time-translation symmetry and thermodynamics , 2014, 1410.4572.

[57]  J. Eisert,et al.  Thermodynamic work from operational principles , 2015, 1504.05056.

[58]  Christine A Muschik,et al.  Entanglement distillation by dissipation and continuous quantum repeaters. , 2010, Physical review letters.

[59]  Paul Skrzypczyk,et al.  Entanglement enhances cooling in microscopic quantum refrigerators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  W. Marsden I and J , 2012 .

[61]  Paul Skrzypczyk,et al.  Extracting work from correlations , 2014, 1407.7765.

[62]  Peter Hänggi,et al.  Specific heat anomalies of open quantum systems. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[63]  J. Cardy,et al.  Time dependence of correlation functions following a quantum quench. , 2006, Physical review letters.

[64]  J. Åberg Fully quantum fluctuation theorems , 2016, 1601.01302.

[65]  Gert-Ludwig Ingold,et al.  Finite quantum dissipation: the challenge of obtaining specific heat , 2008, 0805.3974.

[66]  Rune B. Lyngsø,et al.  Lecture Notes I , 2008 .

[67]  M. Horodecki,et al.  Reversible transformations from pure to mixed states and the unique measure of information , 2002, quant-ph/0212019.

[68]  M. Plenio,et al.  Quantifying coherence. , 2013, Physical review letters.

[69]  Ronnie Kosloff,et al.  Quantum Thermodynamics: A Dynamical Viewpoint , 2013, Entropy.

[70]  N. Gisin,et al.  Experimental entanglement distillation and ‘hidden’ non-locality , 2001, Nature.

[71]  J. Renes,et al.  Beyond heat baths: Generalized resource theories for small-scale thermodynamics. , 2014, Physical review. E.

[72]  M. Esposito,et al.  Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems , 2008, 0811.3717.

[73]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[74]  Charles H. Bennett,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[75]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[76]  J. Gemmer,et al.  From single-shot towards general work extraction in a quantum thermodynamic framework , 2015, 1504.05061.

[77]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[78]  C. J. Adkins Equilibrium thermodynamics: Frontmatter , 1983 .

[79]  Michal Horodecki,et al.  Thermodynamics of Quantum Information Systems — Hamiltonian Description , 2004, Open Syst. Inf. Dyn..

[80]  I. S. Oliveira,et al.  Experimental reconstruction of work distribution and study of fluctuation relations in a closed quantum system. , 2013, Physical review letters.

[81]  Mark M. Wilde,et al.  Work and reversibility in quantum thermodynamics , 2015, Physical Review A.

[82]  Alexandra Olaya-Castro,et al.  Work, heat and entropy production in bipartite quantum systems , 2015, 1507.00441.

[83]  J. Åberg Truly work-like work extraction via a single-shot analysis , 2011, Nature Communications.

[84]  P. Talkner,et al.  Colloquium: Quantum fluctuation relations: Foundations and applications , 2010, 1012.2268.

[85]  J. Herskowitz,et al.  Proceedings of the National Academy of Sciences, USA , 1996, Current Biology.

[86]  A. J. Short,et al.  Clock-driven quantum thermal engines , 2014, 1412.1338.

[87]  Debra J Searles,et al.  Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales. , 2002, Physical review letters.

[88]  F. Brandão,et al.  Reversible Framework for Quantum Resource Theories. , 2015, Physical review letters.

[89]  F. Brandão,et al.  Resource theory of quantum states out of thermal equilibrium. , 2011, Physical review letters.

[90]  Jonathan Oppenheim,et al.  Autonomous Quantum Machines and Finite-Sized Clocks , 2016, Annales Henri Poincaré.

[91]  Markus P. Mueller Correlating Thermal Machines and the Second Law at the Nanoscale , 2017, Physical Review X.