@article{AbiusoHolubecAndersetal.2022,
  author    = {Abiuso, Paolo and Holubec, Viktor and Anders, Janet and Ye, Zhuolin and Cerisola, Federico and Perarnau-Llobet, Marti},
  title     = {Thermodynamics and optimal protocols of multidimensional quadratic Brownian systems},
  series = {Journal of physics communications},
  volume    = {6},
  journal   = {Journal of physics communications},
  number    = {6},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {2399-6528},
  doi       = {10.1088/2399-6528/ac72f8},
  pages     = {15},
  year      = {2022},
  abstract  = {We characterize finite-time thermodynamic processes of multidimensional quadratic overdamped systems. Analytic expressions are provided for heat, work, and dissipation for any evolution of the system covariance matrix. The Bures-Wasserstein metric between covariance matrices naturally emerges as the local quantifier of dissipation. General principles of how to apply these geometric tools to identify optimal protocols are discussed. Focusing on the relevant slow-driving limit, we show how these results can be used to analyze cases in which the experimental control over the system is partial.},
  language  = {en}
}
@article{DieterichKlagesChechkin2015,
  author    = {Dieterich, Peter and Klages, Rainer and Chechkin, Aleksei V.},
  title     = {Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {17},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/17/7/075004},
  pages     = {14},
  year      = {2015},
  abstract  = {Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations (FRs). As prototypes we study three variants of a generic time-fractional Fokker-Planck equation with constant force. Type A generates superdiffusion, type B subdiffusion and type C both super-and subdiffusion depending on parameter variation. Furthermore type C obeys a fluctuation-dissipation relation whereas A and B do not. We calculate analytically the position PDFs for all three cases and explore numerically their strongly non-Gaussian shapes. While for type C we obtain the conventional transient work FR, type A and type B both yield deviations by featuring a coefficient that depends on time and by a nonlinear dependence on the work. We discuss possible applications of these types of dynamics and FRs to experiments.},
  language  = {en}
}
@article{GoychukKharchenko2013,
  author    = {Goychuk, I. and Kharchenko, V. O.},
  title     = {Rocking subdiffusive ratchets origin, optimization and efficiency},
  series = {Mathematical modelling of natural phenomena},
  volume    = {8},
  journal   = {Mathematical modelling of natural phenomena},
  number    = {2},
  publisher = {EDP Sciences},
  address   = {Les Ulis},
  issn      = {0973-5348},
  doi       = {10.1051/mmnp/20138210},
  pages     = {144 -- 158},
  year      = {2013},
  abstract  = {We study origin, parameter optimization, and thermodynamic efficiency of isothermal rocking ratchets based on fractional subdiffusion within a generalized non-Markovian Langevin equation approach. A corresponding multi-dimensional Markovian embedding dynamics is realized using a set of auxiliary Brownian particles elastically coupled to the central Brownian particle (see video on the journal web site). We show that anomalous subdiffusive transport emerges due to an interplay of nonlinear response and viscoelastic effects for fractional Brownian motion in periodic potentials with broken space-inversion symmetry and driven by a time-periodic field. The anomalous transport becomes optimal for a subthreshold driving when the driving period matches a characteristic time scale of interwell transitions. It can also be optimized by varying temperature, amplitude of periodic potential and driving strength. The useful work done against a load shows a parabolic dependence on the load strength. It grows sublinearly with time and the corresponding thermodynamic efficiency decays algebraically in time because the energy supplied by the driving field scales with time linearly. However, it compares well with the efficiency of normal diffusion rocking ratchets on an appreciably long time scale.},
  language  = {en}
}