Abstract
Recently, the fundamental laws of thermodynamics have been reconsidered for small systems. The discovery of the fluctuation relations1,2,3,4,5 has spurred theoretical6,7,8,9,10,11,12,13 and experimental14,15,16,17,18,19,20,21,22,23,24,25 studies. The concept of entropy production has been extended to the microscopic level by considering stochastic trajectories of a system coupled to a heat bath. However, this has not been studied experimentally if there are multiple thermal baths present. Here, we measure, with high precision, the distributions of microscopic entropy production in a single-electron box consisting of two islands with a tunnel junction. The islands are coupled to separate heat baths at different temperatures, maintaining a steady thermal non-equilibrium. We demonstrate that stochastic entropy production8,10,11,12,17,20,25,26 from trajectories of electronic transitions is related to thermodynamic entropy production from dissipated heat in the respective thermal baths. We verify experimentally that the fluctuation relations for both definitions are satisfied. Our results reveal the subtlety of irreversible entropy production in non-equilibrium.
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Acknowledgements
This work has been supported in part by the Academy of Finland though its LTQ (project no. 250280) and COMP (project no. 251748) CoE grants, the European Union Seventh Framework Programme INFERNOS (FP7/2007–2013) under grant agreement no. 308850, the Research Foundation of Helsinki University of Technology, and the Väisälä Foundation. We acknowledge Micronova Nanofabrication Centre of Aalto University for providing the processing facilities and technical support. We thank D. Averin, S. Gasparinetti, F. Hekking, K. Likharev, V. Maisi and M. Meschke for useful discussions.
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J.V.K., O-P.S., Y.Y. and J.P.P. conceived and designed the experiments; J.V.K., O-P.S. and Y.Y. performed the experiments; J.V.K. and M.M. analysed the data. All authors contributed with materials/analysis tools; J.V.K., T.S., M.M., T.A-N. and J.P.P. wrote the paper.
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Koski, J., Sagawa, T., Saira, OP. et al. Distribution of entropy production in a single-electron box. Nature Phys 9, 644–648 (2013). https://doi.org/10.1038/nphys2711
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DOI: https://doi.org/10.1038/nphys2711
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