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

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

Multiwavelength Observations of Gamma-ray Binary Candidates

A rare group of high mass X-ray binaries (HMXBs) are known that also exhibit MeV, GeV, and/or TeV emission ("gamma-ray binaries"). Expanding the sample of gamma-ray binaries and identifying unknown Fermi sources are currently of great interest to the community. Based upon their positional coincidence with the unidentified Fermi sources 1FGL J1127.7-6244c and 1FGL J1808.5-1954c, the Be stars HD 99771 and HD 165783 have been proposed as gamma-ray binary candidates. During Fermi Cycle 4, we have performed multiwavelength observations of these sources using XMM-Newton and the CTIO 1.5m telescope. We do not confirm high energy emission from the Be stars. Here we examine other X-ray sources in the field of view that are potential counterparts to the Fermi sources.Comment: 2012 Fermi Symposium proceedings - eConf C12102

Experimental study of the fluctuation theorem in a nonequilibrium steady state

The fluctuation theorem (FT) quantifies the probability of second law violations in small systems over short time scales. While this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state, there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state. The asymptotic application of the FT to such nonequilibrium steady states has been referred to in the literature as the steady-state fluctuation theorem (or SSFT). In this paper, we demonstrate experimentally the application of the FT to nonequilibrium steady states, using a colloidal particle localized in a translating optical trap. Furthermore, we show, for this colloidal system, that the FT holds under nonequilibrium steady states for all time, and not just in the long time limit, as in the SSFT

Non-equilibrium umbrella sampling applied to force spectroscopy of soft matter

Physical systems often respond on a timescale which is longer than that of the measurement. This is particularly true in soft matter where direct experimental measurement, for example in force spectroscopy, drives the soft system out of equilibrium and provides a non-equilibrium measure. Here we demonstrate experimentally for the first time that equilibrium physical quantities (such as the mean square displacement) can be obtained from non-equilibrium measurements via umbrella sampling. Our model experimental system is a bead fluctuating in a time-varying optical trap. We also show this for simulated force spectroscopy on a complex soft molecule--a piston-rotaxane

Dissipation in monotonic and non-monotonic relaxation to equilibrium

Using molecular dynamics simulations, we study field free relaxation from a non-uniform initial density, monitored using both density distributions and the dissipation function. When this density gradient is applied to colour labelled particles, the density distribution decays to a sine curve of fundamental wavelength, which then decays conformally towards a uniform distribution. For conformal relaxation, the dissipation function is found to decay towards equilibrium monotonically, consistent with the predictions of the relaxation theorem. When the system is initiated with a more dramatic density gradient, applied to all particles, non-conformal relaxation is seen in both the dissipation function and the Fourier components of the density distribution. At times, the system appears to be moving away from a uniform density distribution. In both cases, the dissipation function satisfies the modified second law inequality, and the dissipation theorem is demonstrated