Statistical Mechanics of Time Independent Non-Dissipative Nonequilibrium States

We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are given by the standard Boltzmann weights. In contrast to previous energy landscape treatments, that have been developed specifically for the glass transition, we do not impose an a priori knowledge of the inter-domain population distribution. Assuming that these domains are robust with respect to small changes in thermodynamic state variables we derive a variety of fluctuation formulae for these systems. We verify our theoretical results using molecular dynamics simulations on a model glass forming system. Non-equilibrium Transient Fluctuation Relations are derived for the fluctuations resulting from a sudden finite change to the system's temperature or pressure and these are shown to be consistent with the simulation results. The necessary and sufficient conditions for these relations to be valid are that the domains are internally populated by Boltzmann statistics and that the domains are robust. The Transient Fluctuation Relations thus provide an independent quantitative justification for the assumptions used in our statistical mechanical treatment of these systems.Comment: 17 pages, 4 figures, minor amendment

The rheology of solid glass

As the glass transition is approached from the high temperature side, viewed as a liquid, the properties of the ever more viscous supercooled liquid are continuous functions of temperature and pressure. The point at which we decide to classify the fluid as a solid is therefore subjective. This subjective decision does, however, have discontinuous consequences for how we determine the rheological properties of the glass. We apply the recently discovered relaxation theorem to the time independent, nondissipative, nonergodic glassy state to derive an expression for the phase space distribution of an ensemble of glass samples. This distribution is then used to construct a time dependent linear response theory for aged glassysolids. The theory is verified using molecular dynamics simulations of oscillatory shear for a realistic model glass former with excellent agreement being obtained between the response theory calculations and direct nonequilibrium molecular dynamics calculations. Our numerical results confirm that unlike all the fluid states, including supercooled liquids, a solidglass (in common with crystalline states) has a nonzero value for the zero frequency shear modulus. Of all the states of matter, a supercooled fluid approaching the glass transition has the highest value for the limiting zero frequency shear viscosity. Finally, solidglasses like dilute gases and crystals have a positive temperature coefficient for the shear viscosity whereas supercooled and normal liquids have a negative temperature coefficient.We thank the National Computational Infrastructure NCI for computational facilities and the Australian Research Council ARC for funding

The release of a captive-raised female African Elephant <em>(Loxodonta africana</em>) in the Okavango Delta, Botswana

Wild female elephants live in close-knit matrilineal groups and housing captive elephants in artificial social groupings can cause significant welfare issues for individuals not accepted by other group members. We document the release of a captive-raised female elephant used in the safari industry because of welfare and management problems. She was fitted with a satellite collar, and spatial and behavioural data were collected over a 17-month period to quantify her interactions with the wild population. She was then monitored infrequently for a further five-and-a-half years. We observed few signs of aggression towards her from the wild elephants with which she socialized. She used an area of comparable size to wild female elephants, and this continued to increase as she explored new areas. Although she did not fully integrate into a wild herd, she had three calves of her own, and formed a social unit with another female and her calf that were later released from the same captive herd. We recommend that release to the wild be considered as a management option for other captive female elephants

Verification of time-reversibility requirementfor systems satisfying the Evans-Searles fluctuation theorem

The Evans-Searles fluctuation theorem (ESFT) has been shown to be applicable in the near- and far-from-equilibrium regimes for systems with both constant and time-dependent external fields. The derivations of the ESFT have assumed that the external field has a definite parity under a time-reversal mapping. In the present paper, we confirm that the time-reversibility of the system dynamics is a necessary condition for the ESFT to hold. The manner in which the ESFT fails for systems that are not time-reversible is presented, and results are shown which demonstrate that systems which fail to satisfy the ESFT may still satisfy the Crooks relation (CR)

On the relaxation to nonequilibrium steady states

The issue of relaxation has been addressed in terms of ergodic theory in the past. However, the application of that theory to models of physical interest is problematic, especially when dealing with relaxation to nonequilibrium steady states. Here, we consider the relaxation of classical, thermostatted particle systems to equilibrium as well as to nonequilibrium steady states, using dynamical notions including decay of correlations. We show that the condition known as {\Omega}T-mixing is necessary and sufficient to prove relaxation of ensemble averages to steady state values. We then observe that the condition known as weak T-mixing applied to smooth observables is sufficient for relaxation to be independent of the initial ensemble. Lastly, weak T-mixing for integrable functions makes relaxation independent of the ensemble member, apart from a negligible set of members enabling the result to be applied to observations from a single physical experiment. The results also allow us to give a microscopic derivation of Prigogine's principle of minimum entropy production in the linear response regime. The key to deriving these results lies in shifting the discussion from characteristics of dynamical systems, such as those related to metric transitivity, to physical measurements and to the behaviour of observables. This naturally leads to the notion of physical ergodicity.Comment: 44 pages, 1 figur

The Glass Transition and the Jarzynski Equality

A simple model featuring a double well potential is used to represent a liquid that is quenched from an ergodic state into a history dependent glassy state. Issues surrounding the application of the Jarzynski Equality to glass formation are investigated. We demonstrate that the Jarzynski Equality gives the free energy difference between the initial state and the state we would obtain if the glass relaxed to true thermodynamic equilibrium. We derive new variations of the Jarzynski Equality which are relevant to the history dependent glassy state rather than the underlying equilibrium state. It is shown how to compute the free energy differences for the nonequilibrium history dependent glassy state such that it remains consistent with the standard expression for the entropy and with the second law inequality.Comment: 16 pages, 5 figure

In situ apparatus for the study of clathrate hydrates relevant to solar system bodies using synchrotron X-ray diffraction and Raman spectroscopy

Clathrate hydrates are believed to play a significant role in various solar system environments, e.g. comets, and the surfaces and interiors of icy satellites, however the structural factors governing their formation and dissociation are poorly understood. We demonstrate the use of a high pressure gas cell, combined with variable temperature cooling and time-resolved data collection, to the in situ study of clathrate hydrates under conditions relevant to solar system environments. Clathrates formed and processed within the cell are monitored in situ using synchrotron X-ray powder diffraction and Raman spectroscopy. X-ray diffraction allows the formation of clathrate hydrates to be observed as CO2 gas is applied to ice formed within the cell. Complete conversion is obtained by annealing at temperatures just below the ice melting point. A subsequent rise in the quantity of clathrate is observed as the cell is thermally cycled. Four regions between 100-5000cm-1 are present in the Raman spectra that carry features characteristic of both ice and clathrate formation. This novel experimental arrangement is well suited to studying clathrate hydrates over a range of temperature (80-500K) and pressure (1-100bar) conditions and can be used with a variety of different gases and starting aqueous compositions. We propose the increase in clathrate formation observed during thermal cycling may be due to the formation of a quasi liquid-like phase that forms at temperatures below the ice melting point, but which allows easier formation of new clathrate cages, or the retention and delocalisation of previously formed clathrate structures, possibly as amorphous clathrate. The structural similarities between hexagonal ice, the quasi liquid-like phase, and crystalline CO2 hydrate mean that differences in the Raman spectrum are subtle; however, all features out to 5000cm-1 are diagnostic of clathrate structure.Comment: Astronomy & Astrophysics, in press. 6 page

Sher 25: pulsating but apparently alone

The blue supergiant Sher25 is surrounded by an asymmetric, hourglass-shaped circumstellar nebula, which shows similarities to the triple-ring structure seen around SN1987A. From optical spectroscopy over six consecutive nights, we detect periodic radial velocity variations in the stellar spectrum of Sher25 with a peak-to-peak amplitude of ~12 km/s on a timescale of about 6 days, confirming the tentative detec-tion of similar variations by Hendry et al. From consideration of the amplitude and timescale of the signal, coupled with observed line profile variations, we propose that the physical origin of these variations is related to pulsations in the stellar atmosphere, rejecting the previous hypothesis of a massive, short-period binary companion. The radial velocities of two other blue supergiants with similar bipolar nebulae, SBW1 and HD 168625, were also monitored over the course of six nights, but these did not display any significant radial velocity variations.Comment: 9 pages, 7 figures. Accepted for publication in MNRA