A quantum Otto engine with finite heat baths: energy, correlations, and degradation

We study a driven harmonic oscillator operating an Otto cycle between two thermal baths of finite size. By making extensive use of the tools of Gaussian quantum mechanics, we directly simulate the dynamics of the engine as a whole, without the need to make any approximations. This allows us to understand the non-equilibrium thermodynamics of the engine not only from the perspective of the working medium, but also as it is seen from the thermal baths' standpoint. For sufficiently large baths, our engine is capable of running a number of ideal cycles, delivering finite power while operating very close to maximal efficiency. Thereafter, having traversed the baths, the perturbations created by the interaction abruptly deteriorate the engine's performance. We additionally study the correlations generated in the system, and relate the buildup of working medium-baths and bath-bath correlations to the degradation of the engine's performance over the course of many cycles.

[1]  Kavan Modi,et al.  Quantacell: powerful charging of quantum batteries , 2015, 1503.07005.

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

[3]  Bruno Nachtergaele,et al.  Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems , 2007, 0712.3820.

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

[5]  Eric G. Brown.  Thermal amplification of field-correlation harvesting , 2013, 1309.1425.

[6]  Ronnie Kosloff,et al.  The Quantum Harmonic Otto Cycle , 2016, Entropy.

[7]  G. D. Chiara,et al.  A self-contained quantum harmonic engine , 2017, 1708.07435.

[8]  Gerardo Adesso,et al.  Performance bound for quantum absorption refrigerators. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Armen E Allahverdyan,et al.  Carnot cycle at finite power: attainability of maximal efficiency. , 2013, Physical review letters.

[10]  J. Eisert,et al.  Strong Coupling Corrections in Quantum Thermodynamics. , 2017, Physical review letters.

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

[12]  B. Nachtergaele,et al.  Lieb-Robinson Bounds in Quantum Many-Body Physics , 2010, 1004.2086.

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

[14]  Nicolai Friis,et al.  Passivity and practical work extraction using Gaussian operations , 2016, 1608.04977.

[15]  Nicolas C. Menicucci,et al.  Detectors for probing relativistic quantum physics beyond perturbation theory , 2012, 1212.1973.

[16]  M. Paternostro,et al.  More bang for your buck: Super-adiabatic quantum engines , 2013, Scientific Reports.

[17]  J. Eisert,et al.  Thermal machines beyond the weak coupling regime , 2013, 1310.8349.

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

[19]  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 .

[20]  T. Brandes,et al.  Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping , 2016, 1602.01340.

[21]  Alán Aspuru-Guzik,et al.  Strongly Coupled Quantum Heat Machines. , 2015, The journal of physical chemistry letters.

[22]  Armen E Allahverdyan,et al.  Optimal refrigerator. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  M. Esposito,et al.  Quantum thermodynamics: a nonequilibrium Green's function approach. , 2014, Physical review letters.

[24]  Michael M. Wolf,et al.  An improved Landauer principle with finite-size corrections , 2013, 1306.4352.

[25]  D. Haar,et al.  Statistical Physics , 1971, Nature.

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

[27]  J. Rossnagel,et al.  A single-atom heat engine , 2015, Science.

[28]  R. Onofrio,et al.  Thermalization in open classical systems with finite heat baths , 2008, 0810.3251.

[29]  C. Van den Broeck,et al.  Thermodynamic efficiency at maximum power. , 2005, Physical review letters.

[30]  Daniel Ueltschi,et al.  Entropy and the Quantum , 2010 .

[31]  Masahito Hayashi,et al.  Finite-size effect on optimal efficiency of heat engines. , 2017, Physical review. E.

[32]  H. Callen.  Thermodynamics and an Introduction to Thermostatistics , 1988 .

[33]  Stephanie Wehner,et al.  The maximum efficiency of nano heat engines depends on more than temperature , 2015, Quantum.

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

[35]  Santiago Velasco,et al.  New Performance Bounds for a Finite-Time Carnot Refrigerator , 1997 .

[36]  Florian Mintert,et al.  Performance of a quantum heat engine at strong reservoir coupling. , 2016, Physical review. E.

[37]  Jonathan Oppenheim,et al.  A general derivation and quantification of the third law of thermodynamics , 2014, Nature Communications.

[38]  Giuliano Benenti,et al.  Fundamental aspects of steady-state conversion of heat to work at the nanoscale , 2016, 1608.05595.

[39]  R. Zambrini,et al.  Irreversible work and inner friction in quantum thermodynamic processes. , 2014, Physical review letters.

[40]  Carnot's cycle for small systems: irreversibility and cost of operations , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[41]  Robert W. Spekkens,et al.  Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction , 2011, 1111.5057.

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

[43]  Naoto Shiraishi,et al.  Universal Trade-Off Relation between Power and Efficiency for Heat Engines. , 2016, Physical review letters.

[44]  Nahuel Freitas,et al.  Analytic solution for heat flow through a general harmonic network. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Dominik Janzing,et al.  Thermodynamic limits of dynamic cooling. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  J. Pekola,et al.  Finite-Size Bath in Qubit Thermodynamics , 2016, 1602.00474.

[47]  J. G. Muga,et al.  Transitionless quantum drivings for the harmonic oscillator , 2009, 0912.4178.

[48]  F. Illuminati,et al.  Entanglement in continuous-variable systems: recent advances and current perspectives , 2007, quant-ph/0701221.

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

[50]  Ronnie Kosloff,et al.  Quantum Heat Machines Equivalence, Work Extraction beyond Markovianity, and Strong Coupling via Heat Exchangers , 2016, Entropy.

[51]  A. Leggett,et al.  Quantum tunnelling in a dissipative system , 1983 .

[52]  U. Weiss.  Quantum Dissipative Systems , 1993 .

[53]  K. Okuda,et al.  Work output and efficiency at maximum power of linear irreversible heat engines operating with a finite-sized heat source. , 2013, Physical review letters.

[54]  Bonny L. Schumaker,et al.  Quantum mechanical pure states with gaussian wave functions , 1986 .

[55]  U. Seifert.  First and Second Law of Thermodynamics at Strong Coupling. , 2015, Physical review letters.

[56]  U. Seifert.  Efficiency of autonomous soft nanomachines at maximum power. , 2010, Physical review letters.

[57]  H. Scutaru,et al.  Fidelity for displaced squeezed thermal states and the oscillator semigroup , 1997, quant-ph/9708013.