Die Rolle eingefrorener Unordnung in Arbeits- und Fluktuationstheoremen der stochastischen Thermodynamik

• Antragsteller: Professor Dr. Andreas Engel
• Fachliche Zuordnung: Statistische Physik, Nichtlineare Dynamik, Komplexe Systeme, Weiche und fluide Materie, Biologische Physik
• Förderung: Förderung von 2013 bis 2017
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 233528737

• Erstellungsjahr: 2018

Zusammenfassung der Projektergebnisse

The thermodynamics of small systems rests on probability distributions for thermodynamic quantities like work and entropy. In marked contrast to traditional statistical mechanics, however, not only the centers of these distributions describing the probability of typical realizations are important; relevant information on the physics of the system under consideration is also contained in the tails of these distributions quantifying the often exceedingly small probabilities of rare events. For the important case of the work distribution in driven Langevin systems we have exemplarily shown that results for the center of a distribution not necessarily extend to the tails: whereas the center of the distribution approaches a Gaussian in the quasi-static limit the tails remain exponential for arbitrarily slow driving. For a general characterization of the asymptotic tails of probability distributions methods from large deviation theory are very helpful. We have rederived a long-standing result of Donsker and Varadhan on the level 2 large deviation functional for the empirical density of a class of stochastic processes and extended it to non-equilibrium steady states which are beyond the Donsker-Varadhan theory. These results are somewhat formal but they provide a convenient starting point for further investigations. As an application we investigated the large-deviation properties of Taylor dispersion and found substantial improvement upon the traditional treatment focussing at the second moments of the distribution in case of asymmetric flow fields. Static randomness in small thermodynamic systems may act as information reservoir. This point of view allows a quantitative analysis of the efficiency of Maxwell’s demon type of devices that apparently violate the second law of thermodynamics. Typically, these information reservoirs are idealized in the sense that entropy exchange proceeds without transfer of energy. We have shown that results obtained in this way need qualification if a non-zero amount of energy transduction is taken into account. The problems studied are all part of fundamental research in theoretical physics, i.e. despite being interesting and exciting they are rather special and abstract. Our discussion of Taylor dispersion may be relevant in environmental settings in which very small concentrations of pollutants matter.

Projektbezogene Publikationen (Auswahl)

• J. Stat. Mech., P06004 (2013) “On the work distribution in quasi-static processes”
  J. Hoppenau, A. Engel
  
• EPL 105, 50002 (2014) “On the energetics of information exchange”
  J. Hoppenau, A. Engel
  
• New J. Phys. 18, 083010 (2016) “Level 2 and level 2.5 large deviation functionals for systems with and without detailed balance”
  J. Hoppenau, D. Nickelsen, and A. Engel
  
• Phys. Rev. E 95, 012144 (2017) “Large deviations in Taylor dispersion”
  M. Kahlen, A. Engel, and C. Van den Broeck