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Exact results for the finite time thermodynamic uncertainty relation
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
Number of Authors: 2
2018 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 51, no 11, article id 11LT01Article in journal (Refereed) Published
Abstract [en]

We obtain exact results for the recently discovered finite-time thermodynamic uncertainty relation, for the dissipated work W-d, in a stochastically driven system with non-Gaussian work statistics, both in the steady state and transient regimes, by obtaining exact expressions for any moment of W-d at arbitrary times. The uncertainty function (the Fano factor of W-d) is bounded from below by 2k(B)T as expected, for all times tau, in both steady state and transient regimes. The lower bound is reached at tau = 0 as well as when certain system parameters vanish (corresponding to an equilibrium state). Surprisingly, we find that the uncertainty function also reaches a constant value at large tau for all the cases we have looked at. For a system starting and remaining in steady state, the uncertainty function increases monotonically, as a function of tau as well as other system parameters, implying that the large t value is also an upper bound. For the same system in the transient regime, however, we find that the uncertainty function can have a local minimum at an accessible time tau(m), for a range of parameter values. The large tau value for the uncertainty function is hence not a bound in this case. The non-monotonicity suggests, rather counter-intuitively, that there might be an optimal time for the working of microscopic machines, as well as an optimal configuration in the phase space of parameter values. Our solutions show that the ratios of higher moments of the dissipated work are also bounded from below by 2k(B)T. For another model, also solvable by our methods, which never reaches a steady state, the uncertainty function, is in some cases, bounded from below by a value less than 2k(B)T.

Place, publisher, year, edition, pages
2018. Vol. 51, no 11, article id 11LT01
Keyword [en]
stochastic thermodynamics, non-equilibrium systems, thermodynamic uncertainty relation, entropy production
National Category
Physical Sciences Mathematics
Identifiers
URN: urn:nbn:se:su:diva-153587DOI: 10.1088/1751-8121/aaaa54ISI: 000425341100001OAI: oai:DiVA.org:su-153587DiVA, id: diva2:1190768
Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2018-03-15Bibliographically approved

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Manikandan, Sreekanth K.Krishnamurthy, Supriya
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