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Non-equilibrium thermodynamics at the microscopic scales
Stockholm University, Faculty of Science, Department of Physics.
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

An inherent feature of small systems in contact with thermal reservoirs, be it a pollen grain in water, or an active microbe flagellum, is fluctuations. Even with advanced microscopic techniques, distinguishing active, non-equilibrium processes defined by a constant dissipation of energy to the environment from passive, equilibrium processes is a very challenging task and a vastly developing field of research. For small (microscopic) systems in contact with thermal reservoirs, the experimental / theoretic framework that addresses these fundamental questions, is called stochastic thermodynamics.

In this thesis, we study the stochastic thermodynamics of microscopic machines with colloidal particles as working substances. In particular, we use a path integral based framework to characterize the fluctuations of thermodynamic observables, such as Work, Heat and Entropy production in colloidal heat engines. We obtain exact analytic solutions at finite operational times and the results reveal model independent features of Work and Efficiency fluctuations.

We also discuss the thermodynamic uncertainty relations, which relate current fluctuations in non-equilibrium steady states to the average rate of entropy production. Based on this relation, as well as exact analytical solutions for explicit models, we propose a simple and effective way to infer dissipation from current fluctuations in non-equilibrium systems, from short empirical trajectories.

Finally, we conclude with a discussion on possible extensions of our results.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University , 2020. , p. 86
Keywords [en]
Non-equilibrium statistical Physics, entropy production
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-181029ISBN: 978-91-7911-174-8 (print)ISBN: 978-91-7911-175-5 (electronic)OAI: oai:DiVA.org:su-181029DiVA, id: diva2:1426350
Public defence
2020-06-15, sal FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2020-05-19 Created: 2020-04-24 Last updated: 2020-05-25Bibliographically approved
List of papers
1. Asymptotics of work distributions in a stochastically driven system
Open this publication in new window or tab >>Asymptotics of work distributions in a stochastically driven system
2017 (English)In: European Physical Journal B: Condensed Matter Physics, ISSN 1434-6028, E-ISSN 1434-6036, Vol. 90, no 12, article id 258Article in journal (Refereed) Published
Abstract [en]

We determine the asymptotic forms of work distributions at arbitrary times T, in a class of driven stochastic systems using a theory developed by Nickelsen and Engel (EN theory) [D. Nickelsen and A. Engel, Eur. Phys. J. B 82 , 207 (2011)], which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in path integral form, are characterised by having quadratic augmented actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks fluctuation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial, which also determines the exact moment-generating-function at arbitrary times. We then extend our analysis to a stochastically driven system, studied in references [S. Sabhapandit, EPL 89 , 60003 (2010); A. Pal, S. Sabhapandit, Phys. Rev. E 87 , 022138 (2013); G. Verley, C. Van den Broeck, M. Esposito, New J. Phys. 16 , 095001 (2014)], for both equilibrium and non-equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary T. For dissipated work in the steady state, we compare the large T asymptotic behaviour of our solution to the functional form obtained in reference [New J. Phys. 16 , 095001 (2014)]. In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with numerical simulations. Our solutions are exact in the low noise (beta -> (infinity)) limit.

Keywords
Statistical and Nonlinear Physics
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-150952 (URN)10.1140/epjb/e2017-80432-9 (DOI)000418431900002 ()
Available from: 2018-01-15 Created: 2018-01-15 Last updated: 2020-05-05Bibliographically approved
2. Efficiency Fluctuations in Microscopic Machines
Open this publication in new window or tab >>Efficiency Fluctuations in Microscopic Machines
2019 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 122, no 14, article id 140601Article in journal (Refereed) Published
Abstract [en]

Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a universal theory of efficiency fluctuations at long times, for machines with a finite state space, was developed by Verley et al. [Nat. Commun. 5, 4721 (2014); Phys. Rev. E 90, 052145 (2014)]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the universal features and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two nontrivial models of colloidal engines.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-168343 (URN)10.1103/PhysRevLett.122.140601 (DOI)000463902800004 ()
Available from: 2019-05-08 Created: 2019-05-08 Last updated: 2020-05-05Bibliographically approved
3. Exact results for the finite time thermodynamic uncertainty relation
Open this publication in new window or tab >>Exact results for the finite time thermodynamic uncertainty relation
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.

Keywords
stochastic thermodynamics, non-equilibrium systems, thermodynamic uncertainty relation, entropy production
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-153587 (URN)10.1088/1751-8121/aaaa54 (DOI)000425341100001 ()
Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2020-05-05Bibliographically approved
4. Inferring Entropy Production from Short Experiments
Open this publication in new window or tab >>Inferring Entropy Production from Short Experiments
2020 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 124, no 12, article id 120603Article in journal (Refereed) Published
Abstract [en]

We provide a strategy for the exact inference of the average as well as the fluctuations of the entropy production in nonequilibrium systems in the steady state, from the measurements of arbitrary current fluctuations. Our results are built upon the finite-time generalization of the thermodynamic uncertainty relation, and require only very short time series data from experiments. We illustrate our results with exact and numerical solutions for two colloidal heat engines.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-181026 (URN)10.1103/PhysRevLett.124.120603 (DOI)000521106800003 ()
Available from: 2020-04-24 Created: 2020-04-24 Last updated: 2020-05-05Bibliographically approved

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