Efficiency Statistics and Bounds for Systems with Broken Time-Reversal Symmetry.

Universal properties of the statistics of stochastic efficiency for mesoscopic time-reversal symmetry broken energy transducers are revealed in the Gaussian approximation. We also discuss how the second law of thermodynamics restricts the statistics of stochastic efficiency. The tight-coupling limit becomes unfavorable, characterized by an infinitely broad distribution of efficiency at all times, when time-reversal symmetry breaking leads to an asymmetric Onsager response matrix. The underlying physics is demonstrated through the quantum Hall effect and further elaborated in a triple-quantum-dot three-terminal thermoelectric engine.

[1]  V. Umansky,et al.  Direct observation of a fractional charge , 1997, Nature.

[2]  C. Jarzynski.  Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach , 1997, cond-mat/9707325.

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

[4]  A. Jordan,et al.  Chiral thermoelectrics with quantum Hall edge states. , 2014, Physical review letters.

[5]  Massimiliano Esposito,et al.  Efficiency fluctuations in quantum thermoelectric devices , 2015 .

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

[7]  P. Gaspard.  Multivariate fluctuation relations for currents , 2013 .

[8]  Cohen,et al.  Dynamical Ensembles in Nonequilibrium Statistical Mechanics. , 1994, Physical review letters.

[9]  Evans,et al.  Equilibrium microstates which generate second law violating steady states. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  F Hartmann,et al.  Voltage fluctuation to current converter with Coulomb-coupled quantum dots. , 2015, Physical review letters.

[11]  D. Andrieux,et al.  Fluctuation theorem and Onsager reciprocity relations. , 2004, The Journal of chemical physics.

[12]  M. Büttiker.  Symmetry of electrical conduction , 1988 .

[13]  C. Jarzynski.  Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[14]  Grant M. Rotskoff,et al.  Efficiency and large deviations in time-asymmetric stochastic heat engines , 2014, 1409.1561.

[15]  Udo Seifert,et al.  Multi-terminal thermoelectric transport in a magnetic field: bounds on Onsager coefficients and efficiency , 2013, 1308.2179.

[16]  N. Kiesel,et al.  Out-of-equilibrium thermodynamics of quantum optomechanical systems , 2014, 1412.4803.

[17]  Bart Cleuren,et al.  Stochastic efficiency for effusion as a thermal engine , 2014, 1411.3531.

[18]  P. Solinas,et al.  Distribution of entropy production in a single-electron box , 2013, Nature Physics.

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

[20]  U. Seifert,et al.  Classical Nernst engine. , 2013, Physical review letters.

[21]  Massimiliano Esposito,et al.  The unlikely Carnot efficiency , 2014, Nature Communications.

[22]  Marlan O Scully,et al.  Quantum heat engine power can be increased by noise-induced coherence , 2011, Proceedings of the National Academy of Sciences.

[23]  S. Caplan,et al.  Degree of coupling and its relation to efficiency of energy conversion , 1965 .

[24]  M. Esposito,et al.  Universal theory of efficiency fluctuations. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[26]  M. Esposito,et al.  Efficiency statistics at all times: Carnot limit at finite power. , 2014, Physical review letters.

[27]  Fluctuation theorem for heat transport probed by a thermal probe electrode , 2014, 1403.5582.

[28]  J. Pekola,et al.  Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments , 2014, 1412.0898.

[29]  T. Prosen,et al.  Thermopower with broken time-reversal symmetry , 2011, 1107.1431.

[30]  B. Sothmann,et al.  Quantum heat engines based on electronic Mach-Zehnder interferometers , 2015, 1502.04920.

[31]  Dmitri V. Voronine,et al.  Photosynthetic reaction center as a quantum heat engine , 2013, Proceedings of the National Academy of Sciences.

[32]  C. Jarzynski,et al.  Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies , 2005, Nature.

[33]  Jian-Hua Jiang,et al.  Thermodynamic bounds and general properties of optimal efficiency and power in linear responses. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Jorge Kurchan,et al.  Fluctuation theorem for stochastic dynamics , 1998 .

[35]  E. Lutz,et al.  Experimental verification of Landauer’s principle linking information and thermodynamics , 2012, Nature.

[36]  Giuliano Benenti,et al.  Thermodynamic bounds on efficiency for systems with broken time-reversal symmetry. , 2011, Physical review letters.

[37]  A. Jordan,et al.  Quantum Nernst engines , 2014, 1406.5023.

[38]  C. Broeck,et al.  Stochastic efficiency: five case studies , 2015, 1503.00497.

[39]  D. A. Ritchie,et al.  Harvesting dissipated energy with a mesoscopic ratchet , 2015, Nature Communications.

[40]  Udo Seifert,et al.  Strong bounds on Onsager coefficients and efficiency for three-terminal thermoelectric transport in a magnetic field. , 2013, Physical review letters.