Thermodynamic fluctuations within the Gibbs and Einstein approaches

Rudoi, Yurii Grigor'evich; Sukhanov, A. D.

doi:10.1070/pu2000v043n12abeh000828

Cited by 29 publications

(21 citation statements)

References 37 publications

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“…In the future, a similar study could evaluate the validity of pressure fluctuation relations for canonical systems. 6,8,28…”

Section: Discussionmentioning

confidence: 99%

Temperature fluctuations in canonical systems: Insights from molecular dynamics simulations

Hickman

2016

Phys. Rev. B

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Molecular dynamics simulations of a quasi-harmonic solid are conducted to elucidate the meaning of temperature fluctuations in canonical systems and validate a well-known but frequently contested equation predicting the mean square of such fluctuations. The simulations implement two virtual and one physical (natural) thermostat and examine the kinetic, potential and total energy correlation functions in the time and frequency domains. The results clearly demonstrate the existence of quasi-equilibrium states in which the system can be characterized by a well-defined temperature that follows the mentioned fluctuation equation. The emergence of such states is due to the wide separation of timescales between thermal relaxation by phonon scattering and slow energy exchanges with the thermostat. The quasi-equilibrium states exist between these two timescales when the system behaves as virtually isolated and equilibrium.

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“…In the future, a similar study could evaluate the validity of pressure fluctuation relations for canonical systems. 6,8,28…”

Section: Discussionmentioning

confidence: 99%

Temperature fluctuations in canonical systems: Insights from molecular dynamics simulations

Hickman

2016

Phys. Rev. B

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“…Equations (24) and (25) are interesting because their integration with respect to their frequency arguments makes it possible to obtain in principle the values of asymmetry and excess of equilibrium electrode-potential fluctuations. In line with this, it deserves mention that in the Gibbs statistical thermodynamics, the equations for thermodynamic fluctuations of intensive values (the electrode potential is an intensive value) involve a non-thermodynamic average value which is sufficiently difficult to find and analyze [19].…”

Section: Asymptotics Of Correlationsmentioning

confidence: 87%

“…Based on Eqs. (11),(15),(17), and(19), we have the following expression for the bispectrum(24) Taking into account Eqs (13),(15),(18),. and(20) makes it possible to find the following expression for the trispectrum(25) Equations(24) and(25) are the sought relationships.…”

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confidence: 99%

The fractal theory of electrochemical diffusion noise: Correlations of the third and fourth order

Grafov

2016

Russ J Electrochem

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Based on the Langevin linear stochastic equation, the correlations of the 3rd and 4th order for thermal fluctuations of the electrode potential are studied in an electrochemical ac circuit involving an electric double layer capacitance, a resistance of steady-state diffusion, and a Warburg impedance. The presence of the noisy Warburg impedance in the ac circuit makes the Langevin linear stochastic equation fractal. The analogy with the steady-state diffusion noise and with the noise of the barrierless-activationless slow discharge is used. Equations for bispectrum and trispectrum of electrode-potential activation are shown. It is demonstrated that the intensity of bispectrum and trispectrum is determined exclusively by the noise of the steady-state diffusion resistance if one of frequency arguments in the polyspectrum is zero. It is found that in an electrochemical ac circuit containing the noisy Warburg impedance, the asymptotics of establishment of equilibrium values of asymmetry and excess of electrode-potential fluctuations (thermalization) obeys the power law rather than the exponential law. Furthermore, the excess thermalization proceeds faster as compared with asymmetry thermalization. The performed theoretical analysis of correlations of the 3rd and 4th order of the fractal noise of electrochemical diffusion is of practical interest. For instance, the concepts of the fractal electrochemical noise can be used in the noise diagnostics of devices of electrochemical power engineering and in the noise methods for studying corrosion systems.

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“…On the other hand, the fluctuation of an intensive variable such as force cannot be derived from the partition function when the conjugate extensive variable is fixed, i.e. in a fixed-distance ensemble [24,25]. Here, we use the FJC terminally constrained in full space to illustrate this point.…”

Section: Discussionmentioning

confidence: 99%

Calculation of a fluctuating entropic force by phase space sampling

Waters

Kim

2015

Phys. Rev. E

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A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.

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Thermodynamic fluctuations within the Gibbs and Einstein approaches

Cited by 29 publications

References 37 publications

Temperature fluctuations in canonical systems: Insights from molecular dynamics simulations

Temperature fluctuations in canonical systems: Insights from molecular dynamics simulations

The fractal theory of electrochemical diffusion noise: Correlations of the third and fourth order

Calculation of a fluctuating entropic force by phase space sampling

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