Brownian duet: A novel tale of thermodynamic efficiency

We calculate analytically the stochastic thermodynamic properties of an isothermal Brownian engine driven by a duo of time-periodic forces, including its Onsager coefficients, the stochastic work of each force, and the corresponding stochastic entropy production. We verify the relations between different operational regimes, maximum power, maximum efficiency and minimum dissipation, and reproduce the signature features of the stochastic efficiency. All these results are experimentally tested without adjustable parameters on a colloidal system.

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

[2]  Yonggun Jun,et al.  Virtual potentials for feedback traps. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Ilya Prigogine,et al.  Introduction to Thermodynamics of Irreversible Processes , 1967 .

[4]  P. Visco Work fluctuations for a Brownian particle between two thermostats , 2006, cond-mat/0605069.

[5]  U. Seifert,et al.  Periodic thermodynamics of open quantum systems. , 2016, Physical review. E.

[6]  Massimiliano Esposito,et al.  Ensemble and trajectory thermodynamics: A brief introduction , 2014, 1403.1777.

[7]  John Bechhoefer,et al.  Real-time calibration of a feedback trap. , 2014, The Review of scientific instruments.

[8]  C. Broeck,et al.  Linear stochastic thermodynamics for periodically driven systems , 2015, 1511.03135.

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

[10]  L. Onsager Reciprocal Relations in Irreversible Processes. II. , 1931 .

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

[12]  Karel Proesmans,et al.  Onsager Coefficients in Periodically Driven Systems. , 2015, Physical review letters.

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

[14]  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.

[15]  Dvira Segal,et al.  Efficiency Statistics and Bounds for Systems with Broken Time-Reversal Symmetry. , 2015, Physical review letters.

[16]  Adam E Cohen,et al.  Control of nanoparticles with arbitrary two-dimensional force fields. , 2005, Physical review letters.

[17]  P. S. Pal,et al.  Anomalous Brownian refrigerator , 2015, 1503.02559.

[18]  E. Cohen,et al.  Extension of the fluctuation theorem. , 2003, Physical review letters.

[19]  J. Davies,et al.  Molecular Biology of the Cell , 1983, Bristol Medico-Chirurgical Journal.

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

[21]  H. Fogedby,et al.  A bound particle coupled to two thermostats , 2011, 1104.1539.

[22]  Hua Lee,et al.  Maximum Entropy and Bayesian Methods. , 1996 .

[23]  W. E. Moerner,et al.  Method for trapping and manipulating nanoscale objects in solution , 2005 .

[24]  Udo Seifert,et al.  Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations , 2015, 1505.07771.

[25]  Keiji Saito,et al.  Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field , 2007, 0709.4128.

[26]  P. Reimann Brownian motors: noisy transport far from equilibrium , 2000, cond-mat/0010237.

[27]  J. Parrondo,et al.  Thermodynamics at the microscale: from effective heating to the Brownian Carnot engine , 2016, 1605.04879.

[28]  William H. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

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

[30]  Heat and Charge Current Fluctuations and the Time-Dependent Coefficient of Performance for a Nanoscale Refrigerator , 2016, 1605.03809.

[31]  C. V. Vliet On van Kampen's objections against linear response theory , 1988 .

[32]  Gregory Bulnes Cuetara,et al.  Double quantum dot coupled to a quantum point contact: a stochastic thermodynamics approach , 2015, 1506.04769.

[33]  R. López,et al.  Quantum point contacts as heat engines , 2015, 1506.01613.

[34]  Yonggun Jun,et al.  High-precision test of Landauer's principle in a feedback trap. , 2014, Physical review letters.

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

[36]  Clemens Bechinger,et al.  Realization of a micrometre-sized stochastic heat engine , 2011, Nature Physics.

[37]  J. Parrondo,et al.  Energetics of Brownian motors: a review , 2002 .

[38]  Shu-Kun Lin,et al.  Modern Thermodynamics: From Heat Engines to Dissipative Structures , 1999, Entropy.

[39]  Bart Cleuren,et al.  Power-Efficiency-Dissipation Relations in Linear Thermodynamics. , 2016, Physical review letters.

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

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

[42]  Udo Seifert,et al.  Optimal performance of periodically driven, stochastic heat engines under limited control. , 2016, Physical review. E.

[43]  P. Glansdorff,et al.  Thermodynamic theory of structure, stability and fluctuations , 1971 .

[44]  Kenneth M. Hanson,et al.  Estimators for the Cauchy Distribution , 1996 .

[45]  G. Hummer,et al.  F1-ATPase conformational cycle from simultaneous single-molecule FRET and rotation measurements , 2016, Proceedings of the National Academy of Sciences.

[46]  K. Okuda,et al.  Onsager coefficients of a Brownian Carnot cycle , 2010, 1006.2589.

[47]  F. Michelini,et al.  Heat-charge mixed noise and thermoelectric efficiency fluctuations , 2015, 1510.01056.

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

[49]  Hadrien Vroylandt,et al.  Efficiency fluctuations of small machines with unknown losses. , 2016, Physical review. E.

[50]  D. Petrov,et al.  Brownian Carnot engine , 2014, Nature Physics.

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

[52]  P. S. Pal,et al.  Single-particle stochastic heat engine. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  H. B. G. Casimir,et al.  On Onsager's Principle of Microscopic Reversibility , 1945 .

[54]  G. Marsaglia Ratios of Normal Variables , 2006 .

[55]  Efficiency at maximum power and efficiency fluctuations in a linear Brownian heat-engine model. , 2016, Physical review. E.

[56]  D. Segal,et al.  Full counting statistics of vibrationally assisted electronic conduction: Transport and fluctuations of thermoelectric efficiency , 2015, 1508.02475.

[57]  Koji Okuda,et al.  Onsager coefficients of a finite-time Carnot cycle. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Artem Ryabov,et al.  Maximum efficiency of steady-state heat engines at arbitrary power. , 2016, Physical review. E.

[59]  Injected Power Fluctuations in Langevin Equation , 2001, cond-mat/0106191.