arXiv subjects

Stephen R. Williams

Publications and source records attributed to Stephen R. Williams.

24 records · Page 2Linked to original sources

arXiv2007

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.

cond-mat.stat-mech↗

arXiv2007

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.

cond-mat.stat-mech↗

arXiv2007

Topological Classification of Clusters in Condensed Phases

A methodology is developed to identify clusters in a bulk phase which are topologically equivalent to certain reference clusters. The selected reference clusters are the Morse clusters with 13 or less atoms and the 13 atom clusters found in an FCC and an HCP crystal phase, consisting of an atom and its 12 nearest neighbours. The first step in using the method requires the bond network of the bulk phase to be identified. The bonds may be identified in terms of the distance between the atom pairs or by using a modified Voronoi decomposition, introduced here. We then search for all the 3, 4 and 5 membered shortest path rings and use these to identify some basic clusters. These basic clusters are then combined to identify the above mentioned Morse and crystal clusters. The larger Morse clusters (N>13) may be identified in terms of the basic clusters and the smaller Morse clusters. This work has important applications in studying the energy landscape of a bulk phase. As an example, results from a limited preliminary study on the hard sphere fluid phase are presented.

cond-mat.soft↗

arXiv2007

Deterministic Derivation of NonEquilibrium Free Energy Theorems for Natural Isothermal Isobaric Systems

The nonequilibrium free energy theorems show how distributions of work along nonequilibrium paths are related to free energy differences between the equilibrium states at the end points of these paths. In this paper we develop a natural way of barostatting a system and give the first deterministic derivation of the Crooks and Jarzynski relations for these isothermal isobaric systems. We illustrate these relations by applying them to molecular dynamics simulations of a model polymer undergoing stretching.

cond-mat.stat-mech↗

arXiv2006

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.

cond-mat.stat-mech↗

arXiv2006

Numerical study of the Steady State Fluctuation Relations Far from Equilibrium

A thermostatted dynamical model with five degrees of freedom is used to test both the Evans-Searles and the Gallavotti-Cohen fluctuation relations (ESFR and GCFR respectively). In the absence of an external driving field, the model generates a time independent ergodic equilibrium state with two conjugate pairs of Lyapunov exponents. Each conjugate pair sums to zero. The fluctuation relations are tested numerically both near and far from equilibrium. As expected from previous work, near equilibrium the ESFR is verified by the simulation data while the GCFR is not confirmed by the data. Far from equilibrium where a positive exponent in one of these conjugate pairs becomes negative, we test a conjecture regarding the GCFR made by Gallavotti and co-workers. They conjectured that where the number of nontrivial Lyapunov exponents that are positive becomes less than the number of such negative exponents, then the form of the GCFR needs to be corrected. We show that there is no evidence for this conjecture in the empirical data. In fact as the field increases, the uncorrected form of the GCFR appears to become more accurate. The real reason for this observation is likely to be that as the field increases, the argument of the GCFR more and more accurately approximates the argument of the ESFR. Since the ESFR works for arbitrary field strengths, the uncorrected GCFR appears to become ever more accurate as the field increases. The final point of evidence against the conjecture is that when the smallest positive exponent changes sign, the conjecture predicts a discontinuous change in the "correction factor" for GCFR. We see no evidence for a discontinuity at this field strength; only a gradual improvement of degree of agreement as the field increases.

cond-mat.stat-mech↗