Peter Talkner

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Papers by Peter Talkner

Brownian Motors: Current Fluctuations and Rectification Efficiency

by Eloisa Marchesoni, Peter Talkner, and Jerzy Luczka

Physical Review E, Jan 1, 2004

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Rates and mean first passage times

Physica A: Statistical Mechanics and its Applications, 1997

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Normal versus anomalous self-diffusion in two-dimensional fluids: memory function approach and generalized asymptotic Einstein relation

The Journal of chemical physics, Jan 7, 2014

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized ... more Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

Fluctuation theorems: work is not an observable

Physical review. E, Statistical, nonlinear, and soft matter physics, 2007

The characteristic function of the work performed by an external time-dependent force on a Hamilt... more 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 the Jarzynski work theorem.

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Dynamics of molecular systems: From quantum to classical (in honor of Eli Pollak)

Rate description of Fokker–Planck processes with time-periodic parameters

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First passage time statistics of Brownian motion with purely time dependent drift and diffusion

Systems where resource availability approaches a critical threshold are common to many engineerin... more Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such systems requires solving the associated Fokker-Planck equation subject to an absorbing barrier. Transitional probabilities are derived via the method of

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Microcanonical quantum fluctuation theorems

Physical Review E, 2008

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Quantum fluctuation theorems and generalized measurements during the force protocol

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Generalized measurements of an observable performed on a quantum system during a force protocol a... more Generalized measurements of an observable performed on a quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by M. Campisi, P. Talkner, and P. Hänggi [Phys. Rev. Lett. 105, 140601 (2010); Phys. Rev. E 83, 041114 (2011)], we find that these fluctuation relations are satisfied for projective measurements; however, for generalized measurements special conditions on the operators determining the measurements need to be met. For the Jarzynski equality to hold, the measurement operators of the forward protocol must be normalized in a particular way. The Crooks relation additionally entails that the backward and forward measurement operators depend on each other. Yet, quite some freedom is left as to how the two sets of operators are interrelated. This ambiguity is removed if one considers selective measurements, which are specified by a joint ...

Generalized energy measurements and modified transient quantum fluctuation theorems

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Determining the work which is supplied to a system by an external agent provides a crucial step i... more Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modif...

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Escape rates in periodically driven Markov processes

We present an approximate analytical expression for escape rates of time-dependent driven stochas... more We present an approximate analytical expression for escape rates of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with time-dependent rates. It is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The scheme is carefully tested and yields excellent agreement with three different numerical methods based on the Langevin equation, the Fokker-Planck equation and an integral equation. r 2005 Elsevier B.V. All rights reserved.

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Reaction-rate theory: fifty years after Kramers

Reviews of Modern Physics, 1990

Reaction-rate theory: fifty years after Kramers. Peter Hänggi Lehrstuhl für Theoretische Physik, ... more