title: Open system trajectories specify fluctuating work but not heat.
abstract: Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated. Yet, even though the Hamiltonian of mean force uniquely determines the equilibrium phase space probability density of a strongly coupled open system, the knowledge of this probability density alone is insufficient to determine the Hamiltonian of mean force, needed in constructing the underlying statistical mechanics and thermodynamics. We demonstrate that under the assumption that the Hamiltonian of mean force is known, an extension of thermodynamic structures from the level of averaged quantities to fluctuating objects (i.e., a stochastic thermodynamics) is possible. However, such a construction undesirably also involves a vast ambiguity. This situation is rooted in the eminent lack of a physical guiding principle allowing us to distinguish a physically meaningful theory out of a multitude of other equally conceivable ones.
authors.affiliation: Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany.|Institute of Physics, University of Silesia, 40007 Katowice, Poland.
authors.forename: Peter
authors.initials: P
authors.lastname: Talkner
authors.affiliation: Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86159 Augsburg, Germany.|Nanosystems Initiative Munich, Schellingstr. 4, D-80799 Munich, Germany.|Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia.
authors.forename: Peter
authors.initials: P
authors.lastname: Hänggi