Fluctuation theorems for continuously monitored quantum fluxes

It is shown that quantum fluctuation theorems remain unaffected if measurements of any kind and number of observables are performed during the action of a force protocol. That is, although the backward and forward probabilities entering the fluctuation theorems are both altered by these measurements, their ratio remains unchanged. This observation allows to describe the measurement of fluxes through interfaces and, in this way, to bridge the gap between the current theory, based on only two measurements performed at the beginning and end of the protocol, and experiments that are based on continuous monitoring.Comment: 4 pages, 1 figure. Accepted in Physical Review Letter

Fluctuation relations and rare realizations of transport observables

Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic RC circuit.Comment: 4 pages, 3 figures; v2: minor changes, published versio

Quantum work relations and response theory

A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski equality is recovered in the case this observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity relations are deduced thereof in the linear response regime

Geometric magnetism in open quantum systems

An isolated classical chaotic system, when driven by the slow change of several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations we show that this holds true also for open quantum systems, and provide explicit expressions for those forces in this case. This extends the concept of Berry curvature to the realm of open quantum systems. We illustrate our findings by calculating the geometric magnetism of a damped charged quantum harmonic oscillator transported along a path in physical space in presence of a magnetic field and a thermal environment. We find that in this case the geometric magnetism is unaffected by the presence of the heat bath.Comment: 7 pages. Signs corrected. v3 Accepted in Phys. Rev.

Exact Nonequilibrium Work Generating Function for a Small Classical System

We obtain the exact nonequilibrium work generating function (NEWGF), for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite time interval. The Jarzynski equality (JE), obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work

Thermodynamics as a nonequilibrium path integral

Thermodynamics is a well developed tool to study systems in equilibrium but no such general framework is available for non-equilibrium processes. Only hope for a quantitative description is to fall back upon the equilibrium language as often done in biology. This gap is bridged by the work theorem. By using this theorem we show that the Barkhausen-type non-equilibrium noise in a process, repeated many times, can be combined to construct a special matrix ${\cal S}$ whose principal eigenvector provides the equilibrium distribution. For an interacting system ${\cal S}$, and hence the equilibrium distribution, can be obtained from the free case without any requirement of equilibrium.Comment: 15 pages, 5 eps files. Final version to appear in J Phys.

Nonequilibrium fluctuation-dissipation relations for one- and two-particle correlation functions in steady-state quantum transport

We study the non-equilibrium (NE) fluctuation-dissipation (FD) relations in the context of quantum thermoelectric transport through a two-terminal nanodevice in the steady-state. The FD relations for the one- and two-particle correlation functions are derived for a model of the central region consisting of a single electron level. Explicit expressions for the FD relations of the Green's functions (one-particle correlations) are provided. The FD relations for the current-current and charge-charge (two-particle) correlations are calculated numerically. We use self-consistent NE Green's functions calculations to treat the system in the absence and in the presence of interaction (electron-phonon) in the central region. We show that, for this model, there is no single universal FD theorem for the NE steady state. There are different FD relations for each different class of problems. We find that the FD relations for the one-particle correlation function are strongly dependent on both the NE conditions and the interactions, while the FD relations of the current-current correlation function are much less dependent on the interaction. The latter property suggests interesting applications for single-molecule and other nanoscale transport experiments.Comment: This revised version is now accepted for publication in the Journal of Chemical Physics (March 2014). arXiv admin note: text overlap with arXiv:1305.507

Molecular random walks and invariance group of the Bogolyubov equation

Statistics of molecular random walks in a fluid is considered with the help of the Bogolyubov equation for generating functional of distribution functions. An invariance group of solutions to this equation as functions of the fluid density is discovered. It results in many exact relations between probability distribution of the path of a test particle and its irreducible correlations with the fluid. As the consequence, significant restrictions do arise on possible shapes of the path distribution. In particular, the hypothetical Gaussian form of its long-range asymptotic proves to be forbidden (even in the Boltzmann-Grad limit). Instead, a diffusive asymptotic is allowed which possesses power-law long tail (cut off by ballistic flight length).Comment: 23 pages, no figures, LaTeX AMSART, author's translation from Russian of the paper accepted to the TMPh (``Theoretical and mathematical physics''

On the work distribution for the adiabatic compression of a dilute classical gas

We consider the adiabatic and quasi-static compression of a dilute classical gas, confined in a piston and initially equilibrated with a heat bath. We find that the work performed during this process is described statistically by a gamma distribution. We use this result to show that the model satisfies the non-equilibrium work and fluctuation theorems, but not the flucutation-dissipation relation. We discuss the rare but dominant realizations that contribute most to the exponential average of the work, and relate our results to potentially universal work distributions.Comment: 4 page

Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback

We extend the framework of forward and reverse processes commonly utilized in the derivation and analysis of the nonequilibrium work relations to thermodynamic processes with repeated discrete feedback. Within this framework, we derive a generalization of the detailed fluctuation theorem, which is modified by the addition of a term that quantifies the change in uncertainty about the microscopic state of the system upon making measurements of physical observables during feedback. As an application, we extend two nonequilibrium work relations: the nonequilibrium work fluctuation theorem and the relative-entropy work relation.Comment: 7 pages, 3 figure