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

Probing Proton Strangeness with Time-Like Virtual Compton Scattering

We document that p(gamma,e+e-)p measurements will yield new, important information about the off-shell time-like nucleon form factors, especially in the phi meson region (q^2 = M^2_{phi}) governing the phi N couplings g^{V,T}_{\phi N N}. Calculations for p(gamma,e+e-)p, utilizing vector meson dominance, predict measurable phi enhancements at high |t| compared to the expected phi background production from pi, eta and Pomeron exchange. The phi form factor contribution generates a novel experimental signature for OZI violation and the proton strangeness content. The phi N couplings are determined independently from a combined analysis of the neutron electric form factor and recent high |t| phi photoproduction. The pi, eta and Pomeron transition form factors are also predicted and the observed pi and eta transition moments are reproduced.Comment: 9 pages, 6 figure

The role of local structure in dynamical arrest

Amorphous solids, or glasses, are distinguished from crystalline solids by their lack of long-range structural order. At the level of two-body structural correlations, glassformers show no qualitative change upon vitrifying from a supercooled liquid. Nonetheless the dynamical properties of a glass are so much slower that it appears to take on the properties of a solid. While many theories of the glass transition focus on dynamical quantities, a solid's resistance to flow is often viewed as a consequence of its structure. Here we address the viewpoint that this remains the case for a glass. Recent developments using higher-order measures show a clear emergence of structure upon dynamical arrest in a variety of glass formers and offer the tantalising hope of a structural mechanism for arrest. However a rigorous fundamental identification of such a causal link between structure and arrest remains elusive. We undertake a critical survey of this work in experiments, computer simulation and theory and discuss what might strengthen the link between structure and dynamical arrest. We move on to highlight the relationship between crystallisation and glass-forming ability made possible by this deeper understanding of the structure of the liquid state, and emphasize the potential to design materials with optimal glassforming and crystallisation ability, for applications such as phase-change memory. We then consider aspects of the phenomenology of glassy systems where structural measures have yet to make a large impact, such as polyamorphism (the existence of multiple liquid states), aging (the time-evolution of non-equilibrium materials below their glass transition) and the response of glassy materials to external fields such as shear.Comment: 70 page

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)

Encoding and decoding of dendritic excitation during active states in pyramidal neurons

Neocortical neurons spontaneously fire action potentials during active network states; how are dendritic synaptic inputs integrated into the ongoing action potential output pattern of neurons? Here, the efficacy of barrages of simulated EPSPs generated at known dendritic sites on the rate and pattern of ongoing action potential firing is determined using multisite whole-cell recording techniques from rat layer 5 neocortical pyramidal neurons in vitro. Under quiescent conditions, the somatic impact of proximal (253 +/- 15 microm from soma; n = 28) dendritic barrages of simulated EPSPs was 4.7-fold greater than identical barrages of EPSPs generated from distal (572 +/- 13 microm from soma) sites. In contrast, barrages of proximal simulated EPSPs enhanced the rate of ongoing action potential firing, evoked by somatic simulated EPSPs, by only 1.6-fold more than distal simulated EPSPs. This relationship was apparent across a wide frequency range of action potential firing (6-22 Hz) and dendritic excitation (100-500 Hz). The efficacy of distal dendritic EPSPs was formed by the recruitment of active dendritic processes that transformed the ongoing action potential firing pattern, promoting action potential burst firing. Paired recordings (n = 42) revealed that patterns of action potential firing generated by concerted somatic and distal dendritic excitation reliably and powerfully drove postsynaptic excitation as a result of enhanced reliability of transmitter release during bursts of action potential firing. During active states, therefore, distal excitatory synaptic inputs decisively control the excitatory synaptic output of layer 5 neocortical pyramidal neurons and so powerfully influence network activity in the neocortex

Communication: Broken-ergodicity and the emergence of solid behaviour in amorphous materials

Using a combination of theory and molecular dynamics simulations, we show how solid behaviour emerges in amorphous materials from microscopic considerations. The effect on the systems response to a sudden change in strain, upon entering the history dependent glass state, is focused on. An important symmetry that is always present in a fluid state, is shown to be broken for a simulated history dependent amorphous solid. Details of how this applies to a single sample and an ensemble of independent samples are discussed, along with the dependence on the time scale the system is monitored on

Fluctuation Theorems

Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical relationships for free energy changes. They describe the statistical fluctuations in time-averaged properties of many-particle systems such as fluids driven to nonequilibrium states, and provide some of the very few analytical expressions that describe nonequilibrium states. Quantitative predictions on fluctuations in small systems that are monitored over short periods can also be made, and therefore the fluctuation theorems allow thermodynamic concepts to be extended to apply to finite systems. For this reason, fluctuation theorems are anticipated to play an important role in the design of nanotechnological devices and in understanding biological processes. These theorems, their physical significance and results for experimental and model systems are discussed.Comment: A review, submitted to Annual Reviews in Physical Chemistry, July 2007 Acknowledgements corrected in revisio