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The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes

Description: We show that the nonadditive open systems can be studied in a consistent manner by using a generalized version of S-theorem. This new generalized S-theorem can further be considered as an indication of self-organization in nonadditive open systems as prescribed by Haken. The nonadditive S-theorem is then illustrated by using the modified Van der Pol oscillator. Finally, Tsallis entropy as an equilibrium entropy is studied by using Boltzmann's method of orthodes. This part of dissertation shows that Tsallis ensemble is on equal footing with the microcanonical, canonical and grand canonical ensembles. However, the associated entropy turns out to be Renyi entropy.
Date: August 2008
Creator: Bagci, Gokhan Baris
Partner: UNT Libraries

Complexity as a Form of Transition From Dynamics to Thermodynamics: Application to Sociological and Biological Processes.

Description: This dissertation addresses the delicate problem of establishing the statistical mechanical foundation of complex processes. These processes are characterized by a delicate balance of randomness and order, and a correct paradigm for them seems to be the concept of sporadic randomness. First of all, we have studied if it is possible to establish a foundation of these processes on the basis of a generalized version of thermodynamics, of non-extensive nature. A detailed account of this attempt is reported in Ignaccolo and Grigolini (2001), which shows that this approach leads to inconsistencies. It is shown that there is no need to generalize the Kolmogorov-Sinai entropy by means of a non-extensive indicator, and that the anomaly of these processes does not rest on their non-extensive nature, but rather in the fact that the process of transition from dynamics to thermodynamics, this being still extensive, occurs in an exceptionally extended time scale. Even, when the invariant distribution exists, the time necessary to reach the thermodynamic scaling regime is infinite. In the case where no invariant distribution exists, the complex system lives forever in a condition intermediate between dynamics and thermodynamics. This discovery has made it possible to create a new method of analysis of non-stationary time series which is currently applied to problems of sociological and physiological interest.
Date: May 2003
Creator: Ignaccolo, Massimiliano
Partner: UNT Libraries

PERTURBATION-THEORY RULES FOR COMPUTING THE SELF-ENERGY OPERATOR IN QUANTUM STATISTICAL MECHANICS

Description: Highly convenient rules are given for the general term in the time-independent perturbation-theory expansion for the self-energy operator of quantum statistical mechanics. The rules are derived by starting from the usual formalism involving time-dependent Green's functions. The well-known formulas for thermodynamic quantities in terms of the self-energy operator are included for completeness.
Date: December 17, 1962
Creator: Baym, Gordon & Sessler, Andrew M.
Partner: UNT Libraries Government Documents Department

A NOVEL STATISTICAL BASED APPROACH TO NON-LINEAR MODEL UPDATING USING RESPONSE FEATURES

Description: This research presents a new method to improve analytical model fidelity for non-linear systems. The approach investigates several mechanisms to assist the analyst in updating an analytical model based on experimental data and statistical analysis of parameter effects. The first is a new approach at data reduction called feature extraction. This is an expansion of the ''classic'' update metrics to include specific phenomena or characters of the response that are critical to model application. This is an extension of the familiar linear updating paradigm of utilizing the eigen-parameters or frequency response functions (FRFs) to include such devices as peak acceleration, time of arrival or standard deviation of model error. The next expansion of the updating process is the inclusion of statistical based parameter analysis to quantify the effects of uncertain or significant effect parameters in the construction of a meta-model. This provides indicators of the statistical variation associated with parameters as well as confidence intervals on the coefficients of the resulting meta-model. Also included in this method is the investigation of linear parameter effect screening using a partial factorial variable array for simulation. This is intended to aid the analyst in eliminating from the investigation the parameters that do not have a significant variation effect on the feature metric. Finally an investigation of the model to replicate the measured response variation is examined.
Date: March 1, 2001
Creator: SCHULTZ, J. & AL, ET
Partner: UNT Libraries Government Documents Department

Two-Fold Role of Randomness: A Source of Both Long-Range Correlations and Ordinary Statistical Mechanics

Description: The role of randomness as a generator of long range correlations and ordinary statistical mechanics is investigated in this Dissertation. The difficulties about the derivation of thermodynamics from mechanics are pointed out and the connection between the ordinary fluctuation-dissipation process and possible anomalous properties of statistical systems is highlighted.
Date: December 1998
Creator: Rocco, A. (Andrea)
Partner: UNT Libraries

Non-Poissonian statistics, aging and "blinking'" quantum dots.

Description: This dissertation addresses the delicate problem of aging in complex systems characterized by non-Poissonian statistics. With reference to a generic two-states system interacting with a bath it is shown that to properly describe the evolution of such a system within the formalism of the continuous time random walk (CTRW), it has to be taken into account that, if the system is prepared at time t=0 and the observation of the system starts at a later time ta>0, the distribution of the first sojourn times in each of the two states depends on ta, the age of the system. It is shown that this aging property in the fractional derivative formalism forces to introduce a fractional index depending on time. It is shown also that, when a stationary condition exists, the Onsager regression principle is fulfilled only if the system is aged and consequently if an infinitely aged distribution for the first sojourn times is adopted in the CTRW formalism used to describe the system itself. This dissertation, as final result, shows how to extend to the non-Poisson case the Kubo Anderson (KA) lineshape theory, so as to turn it into a theoretical tool adequate to describe the time evolution of the absorption and emission spectra of CdSe quantum dots. The fluorescence emission of these single nanocrystals exhibits interesting intermittent behavior, namely, a sequence of "light on" and "light off" states, departing from Poisson statistics. Taking aging into account an exact analytical treatment is derived to calculate the spectrum. In the regime fitting experimental data this final result implies that the spectrum of the "blinking" quantum dots must age forever.
Date: August 2004
Creator: Aquino, Gerardo
Partner: UNT Libraries

Final Progress Report for THERMOPHYSICAL PROPERTIES OF FLUIDS AND FLUID MIXTURES

Description: The DOE supported research is a theoretical statistical-mechanical based study of the thermophysical properties of fluids and fluid mixtures. It focuses upon thermodynamic and transport properties in particular. In addition the study covers the development of new ways for predicting the microscopic structure of fluids in a wide range of thermodynamic state parameters, including the critical point.
Date: January 28, 2009
Creator: Stell, George
Partner: UNT Libraries Government Documents Department

Statistical mechanics of sum frequency generation spectroscopy for the liquid-vapor interface of dilute aqueous salt solutions

Description: We demonstrate a theoretical description of vibrational sum frequency generation (SFG) at the boundary of aqueous electrolyte solutions. This approach identifies and exploits a simple relationship between SFG lineshapes and the statistics of molecular orientation and electric field. Our computer simulations indicate that orientational averages governing SFG susceptibility do not manifest ion-specific shifts in local electric field, but instead, ion-induced polarization of subsurface layers. Counterbalancing effects are obtained for monovalent anions and cations at the same depth. Ions held at different depths induce an imbalanced polarization, suggesting that ion-specific effects can arise from weak, long ranged influence on solvent organization.
Date: January 2, 2009
Creator: Noah-Vanhoucke, Joyce; Smith, Jared D. & Geissler, Phillip L.
Partner: UNT Libraries Government Documents Department

Determining the significance of associations between two series of discrete events : bootstrap methods /

Description: We review and develop techniques to determine associations between series of discrete events. The bootstrap, a nonparametric statistical method, allows the determination of the significance of associations with minimal assumptions about the underlying processes. We find the key requirement for this method: one of the series must be widely spaced in time to guarantee the theoretical applicability of the bootstrap. If this condition is met, the calculated significance passes a reasonableness test. We conclude with some potential future extensions and caveats on the applicability of these methods. The techniques presented have been implemented in a Python-based software toolkit.
Date: January 1, 2012
Creator: Niehof, Jonathan T. & Morley, Steven K.
Partner: UNT Libraries Government Documents Department

Measuring Thermodynamic Length

Description: Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information, and Rao's entropy differential metric. Therefore, thermodynamic length is of central interestin understanding matter out of equilibrium. In this Letter, we will consider how to denethermodynamic length for a small system described by equilibrium statistical mechanics and how to measure thermodynamic length within a computer simulation. Surprisingly, Bennett's classic acceptance ratio method for measuring free energy differences also measures thermodynamic length.
Date: September 7, 2007
Creator: Crooks, Gavin E
Partner: UNT Libraries Government Documents Department

Self organizing software research : LDRD final report.

Description: We have made progress in developing a new statistical mechanics approach to designing self organizing systems that is unique to SNL. The primary application target for this ongoing research has been the development of new kinds of nanoscale components and hardware systems. However, this research also enables an out of the box connection to the field of software development. With appropriate modification, the collective behavior physics ideas for enabling simple hardware components to self organize may also provide design methods for a new class of software modules. Our current physics simulations suggest that populations of these special software components would be able to self assemble into a variety of much larger and more complex software systems. If successful, this would provide a radical (disruptive technology) path to developing complex, high reliability software unlike any known today. This high risk, high payoff opportunity does not fit well into existing SNL funding categories, as it is well outside of the mainstreams of both conventional software development practices and the nanoscience research area that spawned it. This LDRD effort was aimed at developing and extending the capabilities of self organizing/assembling software systems, and to demonstrate the unique capabilities and advantages of this radical new approach for software development.
Date: January 1, 2004
Creator: Osbourn, Gordon Cecil
Partner: UNT Libraries Government Documents Department

Fast adaptive flat-histogram ensemble for calculating density of states and enhanced sampling in large systems

Description: We presented an efficient algorithm, fast adaptive flat-histogram ensemble (FAFE), to estimate the density of states (DOS) and to enhance sampling in large systems. FAFE calculates the means of an arbitrary extensive variable U in generalized ensembles to form points on the curve {beta}{sub s}(U) {equivalent_to}{partial_derivative}S(U)/frac/{partial_derivative}U, the derivative of the logarithmic DOS. Unlike the popular Wang-Landau-like (WLL) methods, FAFE satisfies the detailed-balance condition through out the simulation and automatically generates non-uniform ({beta}{sub i}, U{sub i}) data points to follow the real change rate of {beta}{sub s}(U) in different U regions and in different systems. Combined with a U-compression transformation, FAFE reduces the required simulation steps from O(N{sup 3/2}) in WLL to O(N{sup 1/2}), where N is the system size. We demonstrate the efficiency of FAFE in Lennard-Jones liquids with several N values. More importantly, we show its abilities in finding and identifying different macroscopic states including meta-stable states in phase co-existing regions.
Date: January 1, 2009
Creator: Jiang, Yi & Zhou, Xin
Partner: UNT Libraries Government Documents Department

Quantum crooks fluctuation theorem and quantum Jarzynski equality in the presence of a reservoir

Description: We consider the quantum mechanical generalization of Crooks Fluctuation and Jarzynski Equality Theorem for an open quantum system. The explicit expression for microscopic work for an arbitrary prescribed protocol is obtained, and the relation between quantum Crooks Fluctuation Theorem, quantum Jarzynski Equality and their classical counterparts are clarified. Numerical simulations based on a two-level toy model are used to demonstrate the validity of the quantum version of the two theorems beyond linear response theory regime.
Date: January 1, 2008
Creator: Quan, H T & Dong, H
Partner: UNT Libraries Government Documents Department

Hiding quiet solutions in random constraint satisfaction problems

Description: We study constraint satisfaction problems on the so-called planted random ensemble. We show that for a certain class of problems, e.g., graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the planted random ensemble. We study the structural phase transitions and the easy-hard-easy pattern in the average computational complexity. We also discuss the finite temperature phase diagram, finding a close connection with the liquid-glass-solid phenomenology.
Date: January 1, 2008
Creator: Zdeborova, Lenka & Krzakala, Florent
Partner: UNT Libraries Government Documents Department

Planar graphical models which are easy

Description: We describe a rich family of binary variables statistical mechanics models on planar graphs which are equivalent to Gaussian Grassmann Graphical models (free fermions). Calculation of partition function (weighted counting) in the models is easy (of polynomial complexity) as reduced to evaluation of determinants of matrixes linear in the number of variables. In particular, this family of models covers Holographic Algorithms of Valiant and extends on the Gauge Transformations discussed in our previous works.
Date: January 1, 2009
Creator: Chertkov, Michael & Chernyak, Vladimir
Partner: UNT Libraries Government Documents Department

Stochastic Mechanical Systems

Description: To understand the phenomena associated with such stochastic processes and to predict, at least qualitatively, the behavior of mechanical systems within environments which are completely random in time, new mechanical tools are necessary. Fortunately, the derivation of these tools does not necessitate a complete departure from existing theories. In fact, they may be considered as an extension of the well-defined theory of the integral transform, in particular, the exponential Fourier integral transform.
Date: August 1960
Creator: Bost, Robert Berton
Partner: UNT Libraries

HOW DOES A SYSTEM RESPOND WHEN DRIVEN AWAY FROM THERMAL EQUILIBRIUM?

Description: It is widely appreciated that our understanding of non-equilibrium phenomena has not kept pace with its equilibrium counterpart. In recent years, however, consideration of the above question, posed at the microscopic level of statistical mechanics, has yielded some intriguing theoretical results distinguished by two common features. First, they remain valid far from equilibrium, that is, even if the system is disturbed violently from its initial equilibrium state. Second, they incorporate information about the history of the system over some span of time: effectively, these are statistical predictions about what we would see if we could watch a movie of the system filmed at the atomic level, rather than predictions about individual snapshots. To date, this work has been theoretical, though supplemented with numerical simulations. However, in the current issue of PNAS, Hummer and Szabo [1] show how to combine these theoretical advances with single molecule manipulation experiments, so as to extract useful equilibrium information from non-equilibrium laboratory data. What these authors propose amounts to a novel method of deducing the equilibrium mechanical properties of individual molecules.
Date: March 1, 2001
Creator: JARZYNSKI, C.
Partner: UNT Libraries Government Documents Department

EQUILIBRIUM AND NONEQUILIBRIUM FOUNDATIONS OF FREE ENERGY COMPUTATIONAL METHODS

Description: Statistical mechanics provides a rigorous framework for the numerical estimation of free energy differences in complex systems such as biomolecules. This paper presents a brief review of the statistical mechanical identities underlying a number of techniques for computing free energy differences. Both equilibrium and nonequilibrium methods are covered.
Date: March 1, 2001
Creator: JARZYNSKI, C.
Partner: UNT Libraries Government Documents Department