5,007 research outputs found
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
Whales, dolphins, and porpoises of the eastern North Pacific and adjacent Arctic waters: a guide to their identification
This is an identification guide for cetaceans (whales, dolphins, and porpoises), that was designed to assist laymen in identifying cetaceans encountered in eastern North Pacific and Arctic waters. It was intended for use by ongoing cetacean observer programs. This is a revision of an earlier guide with the same title published in 1972 by the Naval Undersa Center and the National Marine Fisheries Service. It includes sections on identifying cetaceans at sea as well as stranded animals on shore. Species accounts are divided by body size and presence or lack of a dorsal fin. Appendices include illustrations of tags on whales, dolphins, and porpoises, by Larry Hobbs; how to record data from observed cetaceans at sea and for stranded cetaceans; and a list of cetacean names in Japanese and Russian. (Document contains 245 pages - file takes considerable time to open
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
A mathematical proof of the zeroth “law” of thermodynamics and the nonlinear Fourier “law” for heat flow
What is now known as the zeroth "law" of thermodynamics was first stated by Maxwell in 1872: at equilibrium, "Bodies whose temperatures are equal to that of the same body have themselves equal temperatures." In the present paper, we give an explicit mathematical proof of the zeroth "law" for classical, deterministic, T-mixing systems. We show that if a body is initially not isothermal it will in the course of time (subject to some simple conditions) relax to isothermal equilibrium where all parts of the system will have the same temperature in accord with the zeroth "law." As part of the derivation we give for the first time, an exact expression for the far from equilibrium thermal conductivity. We also give a general proof that the infinite-time integral, of transient and equilibrium autocorrelation functions of fluxes of non-conserved quantities vanish. This constitutes a proof of what was called the "heat death of the Universe" as was widely discussed in the latter half of the 19th century.We would also like to thank the Australian
Research Council for support of this research. L.R. thanks
the European Research Council, for funding under the European
Community’s (EC) Seventh Framework Programme
(FP7/2007-2013)/ERC Grant Agreement No. 202680
Negative Entropy Production in Oscillatory Processes
Linear irreversible thermodynamics asserts that the instantaneous local
spontaneous entropy production is always nonnegative. However for a
viscoelastic fluid this is not always the case. Given the fundamental status of
the Second Law, this presents a problem. We provide a new derivation of the
Second Law, from first principles, which is valid for the appropriately time
averaged entropy production allowing the instantaneous entropy production to be
negative for short intervals of time. We show that time averages (rather than
instantaneous values) of the entropy production are nonnegative. We illustrate
this using molecular dynamics simulations of oscillatory shear.Comment: 5 pages 2 figure
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