The Steady State Fluctuation Relation for the Dissipation Function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.Comment: 30 pages, 1 figur

Reversibility in nonequilibrium trajectories of an optically trapped particle

The measure of irreversibility as the dissipation function that serves as the quantitative argument in the fluctuation theorem (FT) was investigated. The FT describes the system's thermodynamic irreversibility developed in time from a completely thermodynamically reversibble system at short times to a thermodynamically irreversible one at infinitely long times. It was observed that the ensemble average of ωt was positive definite irrespective of the system for which it was constructed. It was found that the different expressions for ωt can arise in stochastic and deterministic systems

Dissipation and the Relaxation to Equilibrium

Using the recently derived Dissipation Theorem and a corollary of the Transient Fluctuation Theorem (TFT), namely the Second Law Inequality, we derive the unique time independent, equilibrium phase space distribution function for an ergodic Hamiltonian system in contact with a remote heat bath. We prove under very general conditions that any deviation from this equilibrium distribution breaks the time independence of the distribution. Provided temporal correlations decay, and the system is ergodic, we show that any nonequilibrium distribution that is an even function of the momenta, eventually relaxes (not necessarily monotonically) to the equilibrium distribution. Finally we prove that the negative logarithm of the microscopic partition function is equal to the thermodynamic Helmholtz free energy divided by the thermodynamic temperature and Boltzmann's constant. Our results complement and extend the findings of modern ergodic theory and show the importance of dissipation in the process of relaxation towards equilibrium.Comment: 18 pages, no figure

Boundary condition independence of molecular dynamics simulations of planar elongational flow

The simulation of liquid systems in a nonequilibrium steady state under planar elongational flow (PEF) for indefinite time is possible only with the use of the so-called Kraynik-Reinelt (KR) periodic boundary conditions (PBCs) on the simulation cell. These conditions admit a vast range of implementation parameters, which regulate how the unit lattice is deformed under elongation and periodically remapped onto itself. Clearly, nonequilibrium properties of homogeneous systems in a steady state have to be independent of the boundary conditions imposed on the unit cell. In order to confirm the independence of measurable properties of a system under PEF from the particular set of periodic boundary conditions, we compute the Lyapunov spectra, apply the conjugate pairing rule, and carefully analyze the so-called unpaired exponents for an atomic fluid of various sizes and state points. We further compute the elongational viscosity for various implementations of boundary conditions. All our results confirm the independence from KR PBCs for the dynamics of phase-space trajectories and for the transport coefficients

Seismic isolation of Advanced LIGO: Review of strategy, instrumentation and performance

The new generation of gravitational waves detectors require unprecedented levels of isolation from seismic noise. This article reviews the seismic isolation strategy and instrumentation developed for the Advanced LIGO observatories. It summarizes over a decade of research on active inertial isolation and shows the performance recently achieved at the Advanced LIGO observatories. The paper emphasizes the scientific and technical challenges of this endeavor and how they have been addressed. An overview of the isolation strategy is given. It combines multiple layers of passive and active inertial isolation to provide suitable rejection of seismic noise at all frequencies. A detailed presentation of the three active platforms that have been developed is given. They are the hydraulic pre-isolator, the single-stage internal isolator and the two-stage internal isolator. The architecture, instrumentation, control scheme and isolation results are presented for each of the three systems. Results show that the seismic isolation sub-system meets Advanced LIGO\u27s stringent requirements and robustly supports the operation of the two detectors

Formative evaluation of the telecare fall prevention project for older veterans

<p>Abstract</p> <p>Background</p> <p>Fall prevention interventions for community-dwelling older adults have been found to reduce falls in some research studies. However, wider implementation of fall prevention activities in routine care has yielded mixed results. We implemented a theory-driven program to improve care for falls at our Veterans Affairs healthcare facility. The first project arising from this program used a nurse advice telephone line to identify patients' risk factors for falls and to triage patients to appropriate services. Here we report the formative evaluation of this project.</p> <p>Methods</p> <p>To evaluate the intervention we: 1) interviewed patient and employee stakeholders, 2) reviewed participating patients' electronic health record data and 3) abstracted information from meeting minutes. We describe the implementation process, including whether the project was implemented according to plan; identify barriers and facilitators to implementation; and assess the incremental benefit to the quality of health care for fall prevention received by patients in the project. We also estimate the cost of developing the pilot project.</p> <p>Results</p> <p>The project underwent multiple changes over its life span, including the addition of an option to mail patients educational materials about falls. During the project's lifespan, 113 patients were considered for inclusion and 35 participated. Patient and employee interviews suggested support for the project, but revealed that transportation to medical care was a major barrier in following up on fall risks identified by nurse telephone triage. Medical record review showed that the project enhanced usual medical care with respect to home safety counseling. We discontinued the program after 18 months due to staffing limitations and competing priorities. We estimated a cost of $9194 for meeting time to develop the project.</p> <p>Conclusions</p> <p>The project appeared feasible at its outset but could not be sustained past the first cycle of evaluation due to insufficient resources and a waning of local leadership support due to competing national priorities. Future projects will need both front-level staff commitment and prolonged high-level leadership involvement to thrive.</p