Quantum thermodynamic processes: a control theory for machine cycles

The minimal set of thermodynamic control parameters consists of a statistical (thermal) and a mechanical one. These suffice to introduce all the pertinent thermodynamic variables; thermodynamic processes can then be defined as paths on this 2-dimensional control plane. Putting aside coherence we show that for a large class of quantum objects with discrete spectra and for the cycles considered the Carnot efficiency applies as a universal upper bound. In the dynamic (finite time) regime renormalized thermodynamic variables allow to include non-equilibrium phenomena in a systematic way. The machine function ceases to exist in the large speed limit; the way, in which this limit is reached, depends on the type of cycle considered.

[1]  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.

[2]  C. Broeck,et al.  Thermodynamic efficiency at maximum power. , 2005 .

[3]  M. Michel,et al.  Driven spin systems as quantum thermodynamic machines: fundamental limits. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  A. Bejan.  Advanced Engineering Thermodynamics , 1988 .

[5]  T. Cheng.  Relativity, Gravitation, and Cosmology , 2005 .

[6]  T. Jahnke,et al.  Finite-time quantum thermodynamic processes , 2007 .

[7]  Jochen Gemmer,et al.  Quantum Thermodynamic Processes , 2009 .

[8]  Jennifer Sills,et al.  Corrections and clarifications , 2001, BMJ : British Medical Journal.

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

[10]  H T Quan,et al.  Quantum-classical transition of photon-Carnot engine induced by quantum decoherence. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[13]  C. Truesdell,et al.  The Concepts and Logic of Classical Thermodynamics as a Theory of Heat Engines: Rigorously Constructed upon the Foundation Laid by S. Carnot and F. Reech , 1989 .

[14]  Friedemann Tonner,et al.  Autonomous quantum thermodynamic machines. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[16]  Anton Zeilinger,et al.  Decoherence of matter waves by thermal emission of radiation , 2004, Nature.

[17]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[18]  Nobuhiko Saitô,et al.  Statistical Physics , 2021, Major American Universities Ph.D. Qualifying Questions and Solutions - Physics.

[19]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

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

[21]  Small quantum networks operating as quantum thermodynamic machines , 2006, cond-mat/0604202.

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

[23]  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.

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

[25]  Y. Izumida,et al.  Molecular kinetic analysis of a finite-time Carnot cycle , 2008, 0802.3759.

[26]  Gerco Onderwater,et al.  AIP Conf. Proc. , 2009 .

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