title: Fluctuating currents in stochastic thermodynamics. I. Gauge invariance of asymptotic statistics.
abstract: 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.
authors.affiliation: Department of Dynamics of Complex Fluids (DCF), Max Planck Institute for Dynamics and Self-Organization (MPI DS), Am Fassberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Faculty of Physics, Georg-August University Göttingen, 37077 Göttingen, Germany.
authors.forename: Artur
authors.initials: A
authors.lastname: Wachtel
authors.affiliation: Department of Dynamics of Complex Fluids (DCF), Max Planck Institute for Dynamics and Self-Organization (MPI DS), Am Fassberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Faculty of Physics, Georg-August University Göttingen, 37077 Göttingen, Germany.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Vollmer
authors.affiliation: Department of Dynamics of Complex Fluids (DCF), Max Planck Institute for Dynamics and Self-Organization (MPI DS), Am Fassberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Faculty of Physics, Georg-August University Göttingen, 37077 Göttingen, Germany.
authors.forename: Bernhard
authors.initials: B
authors.lastname: Altaner