Polynomial birth--death processes and the second conjecture of Valent

The conjecture of Valent about the type of Jacobi matrices with polynomially growing weights is proved.Comment: 11 page

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

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

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

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.

A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium

There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson formulation (`cyclic changes cost energy'), applied to equilibrium. This formulation of the second law is a property akin to particle conservation (normalization of the wavefunction). It has been stricktly proven for a canonical ensemble, and made plausible for a micro-canonical ensemble. As the derivation does not assume time-inversion-invariance, it is applicable to situations where persistent current occur. This clear-cut derivation allows to revive the ``no perpetuum mobile in equilibrium'' formulation of the second law and to criticize some assumptions which are widespread in literature. The result puts recent results devoted to foundations and limitations of the second law in proper perspective, and structurizes this relatively new field of research.Comment: Revised version. Redundant assumption omitted. Microcanonical ensemble included. Reference added. 7 pages revte

Modeling Maxwell's demon with a microcanonical Szilard engine

Following recent work by Marathe and Parrondo [PRL, 104, 245704 (2010)], we construct a classical Hamiltonian system whose energy is reduced during the adiabatic cycling of external parameters, when initial conditions are sampled microcanonically. Combining our system with a device that measures its energy, we propose a cyclic procedure during which energy is extracted from a heat bath and converted to work, in apparent violation of the second law of thermodynamics. This paradox is resolved by deriving an explicit relationship between the average work delivered during one cycle of operation, and the average information gained when measuring the system's energy

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