Follow @tyc_london for updates from the Thomas Young Centre.
THOMAS YOUNG CENTRE
THE LONDON CENTRE FOR THE THEORY AND SIMULATION OF MATERIALS
Dr Ivan Khaymovich
MPI for Physics of Complex Systems, Dresden, Germany
Energy fluctuations play an important role in small systems. The distribution of entropy production and the work performed under non-equilibrium conditions are governed by fluctuation relations; the second law of thermodynamics applies only for averages over long times or many experiments.
In this talk I will show you how to use simple single-electron circuits as a benchmark to test the concepts of stochastic thermodynamics in experiments. Here the focus will be on fluctuation relations [1,2], Maxwell's demon in form of a Szilard's engine for an electron [3,4]. Single-electron circuits provide a basic set-up for realising a Maxwell’s Demon which utilises one bit of information to extract heat (and work) of about 75% of kT log(2) in a cycle on the average . We will also discuss a recent experiment on an "all-in-one" autonomous Maxwell's demon.
In the final part of the talk we consider the nontrivial analogy between the wide distribution of wave function (WF) amplitudes in disordered systems close to the Anderson localisation transition and the large fluctuations of the dissipated work experienced by systems driven out of equilibrium. We exploit the analogy between the probability distribution function of work dissipated in a driven single-electron box (SEB), the simplest single-electron system, and that of random multifractal WF amplitudes and uncover new relations which generalise the Jarzynski equality. We check the new relations experimentally by measuring the dissipated work in a driven SEB and found a remarkable correspondence. The results published in  represent an universal feature of the work statistics in systems out of equilibrium and help to understand the nature of the symmetry of multifractal exponents in the theory of Anderson localisation.
 O.-P. Saira, Y. Yoon, T. Tanttu, M. Möttönen, D. V. Averin, and J. P. Pekola, Test of Jarzynski and Crooks fluctuation relations in an electronic system, Physical Review Letters 109, 180601 (2012).
 J. V. Koski, T. Sagawa, O.-P. Saira, Y. Yoon, A. Kutvonen, P. Solinas, M. Möttönen, T. Ala-Nissila, and J. P. Pekola, Distribution of Entropy Production in a Single-Electron Box, Nature Physics 9, 644 (2013).
 Jonne V. Koski, Ville F. Maisi, Jukka P. Pekola, and Dmitri V. Averin, Experimental real-ization of a Szilard engine with a single electron, PNAS 111, 13786 (2014).
 Jonne V. Koski, Ville F. Maisi, Takahiro Sagawa, and Jukka P. Pekola, Experimental study of mutual information in a Maxwell Demon, Physical Review Letters 113, 030601 (2014).
 I.M. Khaymovich, J.V. Koski, O.-P. Saira, V.E. Kravtsov, and J.P. Pekola, Multifractality of random eigenfunctions and generalization of Jarzynski equality, Nature Communica-tions 6, 7010 (2015).