Nonequilibrium Reservoir Research Articles

Linear response of hydrodynamically-coupled particles under a nonequilibrium reservoir

A recent experiment driving colloids electromagnetically, by Bérut et al 2014 Europhys. Lett. 107 60004, is an ideal paradigm for illustrating a linear response theory for nonequilibrium overdamped systems including hydrodynamic interactions and, unusually, a reservoir itself out of equilibrium. Indeed, in this setup one finds a nonequilibrium environment in which the mobility and diffusivity of free particles are not simply proportional to each other. We derive both the response to a mechanical forcing and to temperature variations in terms of correlations between an observable and a path-weight action. The time-antisymmetric component of the latter turns out not to be simply proportional to the heat flowing into the environment. These results are visualized with simulations resembling conditions and protocols easily realizable in the experiment, thereby tracing a path for experimental verifications of the theory.

Self-Equilibration of the Diameter of Ga-Catalyzed GaAs Nanowires.

Designing strategies to reach monodispersity in fabrication of semiconductor nanowire ensembles is essential for numerous applications. When Ga-catalyzed GaAs nanowire arrays are grown by molecular beam epitaxy with help of droplet-engineering, we observe a significant narrowing of the diameter distribution of the final nanowire array with respect to the size distribution of the initial Ga droplets. Considering that the droplet serves as a nonequilibrium reservoir of a group III metal, we develop a model that demonstrates a self-equilibration effect on the droplet size in self-catalyzed III-V nanowires. This effect leads to arrays of nanowires with a high degree of uniformity regardless of the initial conditions, while the stationary diameter can be further finely tuned by varying the spacing of the array pitch on patterned Si substrates.

Quantum coherence rather than quantum correlations reflect the effects of a reservoir on a system's work capability.

We consider a model of an optical cavity with a nonequilibrium reservoir consisting of a beam of identical two-level atom pairs (TLAPs) in the general X state. We find that coherence of multiparticle nonequilibrium reservoir plays a central role on the potential work capability of the cavity. We show that no matter whether there are quantum correlations in each TLAP (including quantum entanglement and quantum discord) or not, the coherence of the TLAPs has an effect on the work capability of the cavity. Additionally, constructive and destructive interferences could be induced to influence the work capability of the cavity by adjusting only the relative phase, with which quantum correlations have nothing to do. In this paper, the coherence of the reservoir, rather than the quantum correlations, effectively reflecting the effects of the reservoir on the system's work capability is demonstrated clearly.

Efficiency of heat engines coupled to nonequilibrium reservoirs

We consider quantum heat engines that operate between nonequilibrium stationary reservoirs. We evaluate their maximum efficiency from the positivity of the entropy production and show that it can be expressed in terms of an effective temperature that depends on the nature of the reservoirs. We further compute the efficiency at maximum power for different kinds of engineered reservoirs and derive a nonequilibrium generalization of the Clausius statement of the second law.

A non-equilibrium surface reservoir approach for hybrid DSMC/Navier–Stokes particle generation

An approach for the generation of particles at a hybrid Navier–Stokes/DSMC interface is presented for simple gases and gas mixtures with internal degrees of freedom. DSMC particles generated at a hybrid boundary are assigned thermal velocities using a non-equilibrium surface reservoir approach, in which the fluxes of mass, momentum and energy determined from the Navier–Stokes solution are used to prescribe the appropriate velocity distribution function used in the DSMC particle generation. The non-equilibrium surface reservoir approach is first outlined for a simple (single-species, monatomic) gas, and is then extended to gas mixtures with internal degrees of freedom, in which additional diffusion and internal heat flux terms are included in the Generalized Chapman–Enskog formulation of the perturbation. The significance of the diffusion, shear stress and heat flux breakdown parameters used to compute the perturbation are examined at a hybrid interface within non-equilibrium boundary layer flow, as well as within the breakdown region near a normal shock, in a five-species air gas mixture. The validity of the Chapman–Enskog perturbation at each of these hybrid interfaces is assessed by comparison with the Generalized Chapman–Enskog perturbations. Although a hybrid flowfield solution is not presented, this work provides a rigorous approach for non-equilibrium particle generation involving general hybrid particle/continuum studies of hypersonic flows.

An Addendum to “Detailed Balance has a Counterpart in Nonequilibrium Steady States”

Transition rates in continuously driven steady states (relevant to sheared complex fluids) were derived in Evans (2004, 2005) by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the system be used to describe it. This implies that the (nonequilibrium) reservoir, to which the system is weakly coupled, is fully characterized by its mean energy and mean flux. While we expect the resulting prescription for the rates in continuous- and discretized-time models to be equivalent, it is not trivial to see this from the expression for the rates derived in Evans (2005). We demonstrate this equivalence for a model of activated processes solved previously for continuous time (Evans 2005), thus demonstrating consistency of the theory.

Quantum Zeno and anti-Zeno effect of a nanomechanical resonator measured by a point contact

The occurrence of either the quantum Zeno effect (QZE) or anti-Zeno effect (AZE) resulting from the short-time behavior of the environment-induced decoherence for quantum Brownian motion (QBM) model has been discussed [S. Maniscalco, J. Piilo, and K. A. Suominen, Phys. Rev. Lett. 97, 130402 (2006)]. We discuss here while the shuttering time period (length) of the frequent observations is changed, the system of interest, i.e., a nanomechanical oscillator, will undergo a QZE to AZE crossover. Instead of interacting with an equilibrium bosonic bath in a QBM model, we investigate the occurrence of either QZE or AZE of a nanomechanical oscillator coupled to a nonequilibrium fermionic reservoir [quantum point contact (QPC) detector as a measuring device]. We find that Zeno and anti-Zeno behaviors depend on the values of the system and reservoir parameters such as the oscillator frequency, energy cutoff, bias voltage, and reservoir temperature.

Detailed balance has a counterpart in non-equilibrium steady states

When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is theoretically well founded. Hypothesising ergodicity constrains the transition rates in driven steady states to respect relations analogous to, but different from the equilibrium principle of detailed balance. The constraints arise from demanding that the design of any model system contains no information extraneous to the microscopic laws of motion and the macroscopic observables. This prevents over-description of the non-equilibrium reservoir, and implies that not all stochastic equations of motion are equally valid. The resulting recipe for transition rates has many features in common with equilibrium statistical mechanics.

Gasdynamic Instrumentation of High Enthalpy Flows

Techniques for making measurements of gas properties in supersonic plasmas generated by continuous thermal arc heaters and crossed field accelerators are described: Specifically, measurements of static pressure, total pressure, flow velocity, local mass flow, and local total enthalpy. The use of these measurements together with the relationships between the gasdynamic parameters such as temperature, pressure, density, specific heat, sound speed, Mach number, and degree of dissociation and ionization are discussed. When the gas is out of equilibrium, as it is in crossed field accelerator plumes produced to date and in many thermal arc jets, the number of independent measurements required to determine the gas properties unambiguously is three plus one for each non-equilibrium energy reservoir. Previously described diagnostic techniques for plasma jets, have relied upon known reservoir conditions and upon the use of an effective specific heat ratio. However these assumptions cannot be made for crossed field accelerator plumes because reservoir conditions are not known and because large fractions of the gas energy may be invested in non-equilibrium energy reservoirs. For this reason the analytical treatment of the measurements is important. Results obtained in argon plumes using velocity, static pressure, total pressure, local mass flow, and local total enthalpy probes are presented. Gas properties determined from these measurements are given, and the degree of reliability of the measurements is ascertained by cross-checks wherever possible.