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Topic: Fluctuation theorem

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	Fluctuation dissipation theorem - Wikipedia, the free encyclopedia
		In statistical physics, the fluctuation dissipation theorem is derived from the assumption that the response of a system in thermodynamic equilibrium to a small external perturbation is the same as its response to a spontaneous fluctuation.
		For example, Einstein in his 1905 paper on Brownian motion noted that the same random forces which cause the erratic motion of a particle in Brownian motion would also cause drag if the particle were pulled through the fluid.
		The theorem is based on fields that are weak relative to the potential of molecular interaction so that rates of relaxation are not affected by the applied field.
	en.wikipedia.org /wiki/Fluctuation_dissipation_theorem (390 words)

	Fluctuation theorem - Wikipedia, the free encyclopedia
		Fluctuations in the velocity were recorded that were opposite to what the second law of thermodynamics would dictate for macroscopic systems.
		The fluctuation theorem is of fundamental importance to nonequilibrium statistical mechanics.
		When combined with the central limit theorem, the FT also implies the famous Green-Kubo relations for linear transport coefficients, close to equilibrium.
	en.wikipedia.org /wiki/Fluctuation_theorem (1429 words)

	Chapter 5
		The Fluctuation-Dissipation Theorem proposes that there is an explicit relationship between molecular dynamics at thermal equilibrium and the macroscopic response that is observed in a dynamic measurement.
		Random, thermal and density fluctuations occur due to the motion of molecules at a finite temperature.
		The reason to discuss the fluctuation dissipation theorem in the context of this class is that it is the fundamental justification for the development of molecular scale models of polymer dynamics as indicators of bulk dynamic response.
	www.eng.uc.edu /~gbeaucag/Classes/Physics/DynChapter5html/Chapter5.html (1331 words)

	Computer Models Demonstrating the Fundamentals of Optical Tweezers and the Fluctuation Theorem for Small Systems Under ...
		In addition, a visual demonstration of the fluctuation theorem (FT), a theorem that gives the probability of violations of the Second Law of Thermodynamics for small systems under short time scales, was also created.
		A visual depiction for fluctuation theorem was also created in order to demonstrate and help assist scientists and engineers in the intricacies of experimentation dealing with FT. Each is a comprehensive portrayal of their respective areas of research.
		The fluctuation theorem gives an analytical expression in order to determine the probability, in a non-equilibrium system of finite size observed for a finite time, that the dissipative flux will flow in the reverse direction to that required by the second law of thermodynamics (Ayton et al.
	www.rvgs.k12.va.us /electives/trap/students/ssarin/VJASPaper.htm (3319 words)

	The Tom Bearden Website
		To put this on a scientific basis, Evans and Searles produced the rigorous fluctuation theorem, to deal with the statistical fluctuations that occur, generating reversals (negentropy instead of positive entropy).
		Advances the transient fluctuation theorem which predicts appreciable and measurable violations of the second law of thermodynamics for small systems over short time scales.
		The fluctuation theorem was further generalized by Crooks.
	www.cheniere.org /correspondence/122602.htm (1716 words)

	The Tom Bearden Website
		This paper places the statistical fluctuations on a rigorous basis, the advances that basis, called the fluctuation theorem.
		In a fluctuation, the reactions in a fluctuation run backwards, and so negentropy can be produced for a short time instead of entropy.
		This paper further generalized the fluctuation theorem, extending its range of application.
	www.cheniere.org /correspondence/011403a.htm (1992 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		The relation (\ref{entproform2}) is known as the steady state fluctuation theorem (SSFT) and states a symmetry in the fluctuations of the entropy dissipation in a stationary nonequilibrium steady state.
		It is however unclear what is the meaning of their entropy production operator.\\ A related quantum Jarzynski relation was studied in \cite{DM}.\\ Besides the fluctuation theorem, we also describe a new approach to the study of heat conduction in the quantum weak coupling limit.
		The current fluctuations we define in our model, agree with the expressions of \cite{LS2} as far as the mean currents and the Green-Kubo formula is concerned.
	www.ma.utexas.edu /mp_arc/papers/05-159 (3257 words)

	INI : Abstracts : PDSW02 : The fluctuation & nonequilibrium free energy theorems, theory & experiment (Site not responding. Last check: 2007-10-22)
		We discuss a number of simple consequences of the Fluctuation Theorems including the Second Law Inequality, the Kawasaki Identity and the fact that the dissipation function which is the subject of the FT, is a nonlinear generalization of the spontaneous entropy production, that is so central to linear irreversible thermodyanamics.
		2 The Fluctutation Theorem: In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in small thermostatted nonequilibrium systems which are observed for a short period of time.
		Quantitative predictions made by the Fluctuation Theorem regarding the probability of Second Law `violations' have been confirmed experimentally, both using molecular dynamics computer simulation and very recently in two laboratory experiments[1] which employed optical tweezers.
	www.newton.cam.ac.uk /programmes/PDS/Abstract2/evans.html (312 words)

	ipedia.com: Fluctuation dissipation theorem Article (Site not responding. Last check: 2007-10-22)
		In statistical physics, the fluctuation dissipation theorem states that a change or fluctuation in a system will be dissipated as the system returns to equilibrium.
		A basic premise or theorem of statistical thermodynamics on which such predictions are based is the fluctuation dissipation theorem.
		It proposes that there is an explicit relationship between molecular dynamics at thermal equilibrium, and the macroscopic response that is observed in a dynamic measurement.
	www.ipedia.com /fluctuation_dissipation_theorem.html (222 words)

	Non-equilibrium
		While in each area of research the fluctuations have very different origins, in many cases the evolution equation governing the system of interest can be approximated by a suitable stochastic differential equation.
		The fluctuation term (i.e., the external noise) is always characterized by its associated functional, and the "dissipation" by an arbitrary memory kernel.
		Nevertheless, if the system is far away from equilibrium, the fluctuation-dissipation theorem does not apply and in general the Gaussian assumption is not a good candidate to describe the fluctuations of the system.
	www.arteuna.com /ManuelCaceres/Non-equi.htm (772 words)

	Fluctuation theorem: Encyclopedia topic (Site not responding. Last check: 2007-10-22)
		This theorem (FT) gives a mathematical expression for the probability ratio that time-averaged irreversible entropy production[1], takes on a value, A, to the opposite value, −A, in systems away from equilibrium.
		When combined with the central limit theorem (central limit theorem: more facts about this subject), the FT also implies the famous Green-Kubo relations (Green-Kubo relations: green-kubo relations give exact mathematical expression for transport coefficients in terms...
		[follow hyperlink for more...]) - there is a deep connection between the fluctuation theorem and the Green-Kubo relations for linear transport coefficients - like shear viscosity (viscosity: Resistance of a liquid to sheer forces (and hence to flow)) or thermal conductivity (thermal conductivity: in physics, thermal conductivity, λ, is the quantity of heat transmitted,...
	www.absoluteastronomy.com /reference/fluctuation_theorem (1304 words)

	Physics of thermal noise
		The first clear statement of the theorem in its general form is usually credited to Callen and his collaborators.[4] This powerful theorem describes the fluctuations of any linear system in thermal equilibrium at a temperature T.
		The Fluctuation-Dissipation Theorem itself is an established part of the field of non-equilibrium statistical mechanics.
		But the linkage of the theorem with the phenomenology of internal friction in materials, as described in the P.I.'s 1990 paper,[5] has some surprising features.
	physics.syr.edu /~gravlab/gravity/node3.html (539 words)

	Physics: On the Crooks Fluctuation Theorem
		New work describes a single-molecule experiment that not only validates one prominent recent postulate, known as the "Crooks fluctuation theorem", but also provides a new method for quantifying the difference in equilibrium free energy -- the useful work expected to be extracted from a system -- between two biomolecular states.
		The Crooks fluctuation theorem (CFT) describes the exchange of energy between a system and its environment in forward and reverse processes.
		At a given speed, the work required to move the plunger between two well-defined states is always the same: viewed microscopically, the resistance to the motion is just the statistically averaged effect of many collisions between the plunger and the fast-moving molecules of the fluid.
	scienceweek.com /swbb/messages/bb306.htm (314 words)

	Non-equilibrium statistical mechanics (Site not responding. Last check: 2007-10-22)
		The relation between the response function Chi and the autocorrelation function C is regulated in equilibrium systems by the fluctuation dissipation theorem.
		Indeed, from the relation between Chi and C it is possible to define an effective temperature, which generalizes the ordinary definition of the equilibrium temperature and posses the correct properties (for instance the zero theorem is obeyed).
		Moreover, in the case of aging systems, a theorem can be proved which relates dynamical quantities like Chi and C to some properties of the equilibrium state at the same temperature.
	www.sa.infn.it /Groups/Homepage.asp?9 (205 words)

	Fluctuation Theorem for stochastic dynamics - Kurchan (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		In such a context all non-trivial ergodic theory issues are by-passed, and the theorem takes a particularly simple form.
		The goal of this paper is to continue and to extend the analysis of [32] mostly via specific illustrative examples....
		Kurchan, J.: Fluctuation Theorem for stochastic dynamics, preprint cond-mat@ xyz.
	citeseer.ist.psu.edu /159916.html (433 words)

	papers
		That observation, made since long, is here rigorously analyzed with special care to reconcile the application of Liouville's theorem (for a finite number of particles) with the condition of autonomous macroscopic evolution (sharp only in the limit of infinite scale separation); and to evaluate the presumed necessity of a semigroup property for the macroscopic evolution.
		We give a generalization of fluctuation identities and inequalities for the entropy production when the microscopic dynamics preserves the phase space volume but is not assumed to be dynamically reversible.
		Fluctuation identities describing the relation between entropy production and its time-reversal must however be changed and now involve the time-reversed dynamics.
	itf.fys.kuleuven.ac.be /~christ/pub/papers.html (4769 words)

	Fluctuation theorem for a single enzym or molecular motor
		Fluctuation theorem for a single enzym or molecular motor
		Cyclically operating enzyms and molecular motors are shown to be restricted non-linearly by a fluctuation theorem that basically relates the number of backward steps to that of forward steps.
		Only if the rates obey a quasi-equilibrium form in terms of chemical potentials and mechanical load, this fluctuation theorem becomes the usual one for entropy fluctuations.
	www.edpsciences.org /articles/epl/abs/2005/07/epl8680/epl8680.html (161 words)

	CRISP: Research Project, Valek
		Martin [1986] suggested that the resistance of such plasmas could be due to chaotic diffusion of the particles in phase space.
		The dissipative response of a system near equilibrium to an external force is related to the average fluctuation of the system from equilibrium.
		The equilibrium fluctuations are measured by the current density correlation function:
	www.phy.ilstu.edu /CRISP/valek.html (663 words)

	Math Seminars (Site not responding. Last check: 2007-10-22)
		Fluctuations of the entropy production in non equilibrium statistical systems have been investigated in analytical, numerical and experimental works due to the Fluctuation Theorem.
		This theorem predicts a symmetry for the large fluctuation functional of the entropy production that many believe to be valid well beyond the range of validity of the hypotheses under which one can obtain a rigorous proof.
		Some recent numerical simulations on deterministic systems with singularities or stochastic systems gave rise to questions on the applicability and form of the Fluctuation Theorem.
	www.math.psu.edu /dynsys/abstracts-2006/bonetto.html (111 words)

	SATS-Symposium-Denis Evans (Site not responding. Last check: 2007-10-22)
		The Fluctuation Theorem states that the probability that the time averaged entropy production is equal to a value A, divided by the probability that it takes the value -A, is simply the exponential of At.
		The Fluctuation Theorem senses a direction of time that is not present in dynamics, and so for over 100 years the resolution of how you get irreversible macroscopic behaviour from reversible equations of motion – whether it be quantum mechanics or classical mechanics makes no difference – has been an unresolved question.
		What the Fluctuation Theorem does is to quantify your probabilities of losing at the casino as an ensemble average of the amount of time that you spend at the tables.
	www.science.org.au /sats2003/evans.htm (3006 words)

	Web Lectures: Gabriela Gonzalez (Site not responding. Last check: 2007-10-22)
		This talk grew out of her earlier thesis on the fluctuation-dissipation theorem, an important theorem on the power-frequency distribution of Brownian motion in different systems.
		The theorem represents a fundamental noise limitation on all measurements which she applies here to the analysis of a gravity wave interferometer.
		The talk spends about equal time on the theorem and its interesting history, and the application of this theorem to a system for gravity wave detection.
	physics.hyperjeff.net /lectures/gonzalez.01.html (275 words)

	Colloquia
		In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in small thermostatted nonequilibrium systems which are observed for a short period of time.
		Quantitative predictions made by the Fluctuation Theorem regarding the probability of Second Law "violations" have been confirmed experimentally, both using molecular dynamics computer simulation and very recently in two laboratory experiments [1] which employed optical tweezers.
		[2]"The Fluctuation Theorem" by Denis J Evans and Debra J Searles, Advances in Physics, 51, 1529-1585(2002).
	www.phys.unsw.edu.au /SCHOOL_INFORMATION/COLLOQUIA/2005/may26_2005.html (203 words)

	Römer, Rudolf A.; Ziesche, Paul : Hellmann-Feynman theorem and fluctuation-correlation analysis of the ...
		Exploiting the results of the exact solution for the ground state of the one-dimensional spinless quantum gas of Fermions and impenetrable Bosons with the $\mu/x_{ij}^2$ particle-particle interaction, the Hellmann-Feynman theorem yields mutually compensating divergences of both the kinetic and the interaction energy in the limiting case $\mu {\to}- {1/4}$.
		These divergences result from the peculiar behavior of both the momentum distribution (for large momenta) and the pair density (for small inter-particle separation).
		They are compared with each other and with reference-free, short-range correlation-measuring ratios of the kinetic and potential energies.
	www.mathematik.tu-chemnitz.de /preprint/2000/SFB393_24.html (237 words)

	Demetrius at The Australian National University: Item 1885/40714
		The Fluctuation Theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics.
		In the present paper we show that the Fluctuation Theorem is also valid for a class of stochastic nonequilibrium systems.
		The Theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics.
	hdl.handle.net /1885/40714 (120 words)

	PHYSICS: ON VALIDATION OF THE CROOKS FLUCTUATION THEOREM (Site not responding. Last check: 2007-10-22)
		New work[1] describes a single-molecule experiment that not only validates one prominent recent postulate, known as the "Crooks fluctuation theorem", but also provides a new method for quantifying the difference in equilibrium free energy -- the useful work expected to be extracted from a system -- between two biomolecular states.
		The much-improved experimental access to the energy fluctuations of small systems and the formulation of the principles that govern both energy exchanges and their statistical excursions are starting to shed light on the unique properties of microscopic systems.
		Ultimately, the knowledge physicists are gaining with their new experimental and theoretical tools may serve as the basis for a theory of the nonequilibrium thermodynamics of small systems.
	scienceweek.com /2005/sw051111-1.htm (1541 words)

	Mathematical Physics Seminar
		We make use of the Lyapunov spectra to study a fluctuation relation which had been proposed to extend the ``fluctuation theorem'' to strongly dissipative systems.
		Preliminary results towards the formulation of a local version of the fluctuation formula are also presented.
		Abstract-The (Cohen-Galavotti) fluctuation theorem refers to a symmetry of the fluctuation of the entropy production in a stationary nonequilibrium state.
	www.math.rutgers.edu /~lebowitz/SEMINAR/oct02_schedule.html (1080 words)

	Matrix Fluctuation-Dissipation Theorem: Application to Quantum Relaxation Phenomena (Site not responding. Last check: 2007-10-22)
		We recently derived a matrix fluctuation-dissipation (MFD) theorem, which directly relates the spectral intensities to the eigenvalue fluctuations of a quantum system.
		MFD is a microcanonical version of the fluctuation-dissipation theorem for a single high-energy state embedded in a dissipative quantum-mechanical bath.
		This is useful in applications to vibrational relaxation, which can be exactly described by the MFD formula if a single initial state carries all the oscillator strength.
	pubs.acs.org /cgi-bin/abstract.cgi/jpchax/1996/100/i30/abs/jp960442q.html (181 words)

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