Fluctuating currents in stochastic thermodynamics. I. Gauge invariance of asymptotic statistics
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Wachtel, Artur[Georg-August-Universität Göttingen > Faculty of Physics > > ; Max Planck Institute for Dynamics and Self-Organization > Dynamics of Complex Fluids]
Vollmer, Jürgen[Georg-August-Universität Göttingen > Faculty of Physics > > ; Max Planck Institute for Dynamics and Self-Organization > Dynamics of Complex Fluids]
Altaner, Bernhard[Georg-August-Universität Göttingen > Faculty of Physics > > ; Max Planck Institute for Dynamics and Self-Organization > Dynamics of Complex Fluids]
[en] Stochastic thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from antisymmetric jump observables defined on the edges of the graph representing the network of states. The asymptotic statistics of such currents are characterized by scaled cumulants. In the present work, we use the algebraic and topological structure of Markovian models to prove a gauge invariance of the scaled cumulant-generating function. Exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals. We discuss how our approach generalizes the Schnakenberg decomposition of the average entropy-production rate, and how it unifies previous work. The application of our results to concrete models is presented in an accompanying publication.
"Center for Earth System Research and Sustainability (CliSAP)" at the KlimaCampus Hamburg ; Ludwig Prandtl internship - FOKOS e. V., Gottingen
The authors thank M. Polettini, F. Telschow, and H. Touchette for insightful discussions. F. Angeletti provided useful comments on the manuscript. A.W. is grateful for support from a Ludwig Prandtl internship awarded by FOKOS e. V., Gottingen, and to M. Esposito for his support. J.V. acknowledges support from a research grant from the "Center for Earth System Research and Sustainability (CliSAP)" at the KlimaCampus Hamburg, while the final version of this manuscript was drafted.
[Georg-August-Universität Göttingen > Faculty of Physics > > ; Max Planck Institute for Dynamics and Self-Organization > Dynamics of Complex Fluids]
