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The characteristic function of the work performed by an external time-dependent force on a Hamiltonian quantum system is identified with the time-ordered correlation function of the exponentiated system's Hamiltonian. A similar expression is obtained for the averaged exponential work which is related to the free energy difference of equilibrium systems by(More)
Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars the reader is guided through a self-contained exposition of the theory and applications of quantum fluctuation(More)
The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two-dimensional periodic channels, exhibiting periodically varying cross-sections. The particles in(More)
We propose a numerical integration scheme to solve stochastic differential equations driven by Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches(More)
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(More)
A brief history is presented, outlining the development of rate theory during the past century. Starting from Arrhenius [Z. Phys. Chem. 4, 226 (1889)], we follow especially the formulation of transition state theory by Wigner [Z. Phys. Chem. Abt. B 19, 203 (1932)] and Eyring [J. Chem. Phys. 3, 107 (1935)]. Transition state theory (TST) made it possible to(More)
Based on the observation that the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment is the difference between the free energy of the total system and that of the bare environment, the validity of the Crooks theorem and of the Jarzynski equality is extended to open quantum systems. No restrictions on the(More)
We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems (Campisi et al 2009 Phys. Rev. Lett. 102 210401), by applying them to a solvable model of an open quantum system. The central role played by the thermodynamic partition function of the open quantum system, a two-level fluctuator with a strong quantum(More)
The statistics of transitions between the metastable states of a periodically driven bistable Brownian oscillator are investigated on the basis of a two-state description by means of a master equation with time-dependent rates. The theoretical results are compared with extensive numerical simulations of the Langevin equation for a sinusoidal driving(More)