Effective temperature and fluctuation-dissipation theorem in athermal granular systems:A review

The definition and the previous measurements of a dynamics-relevant temperature-like quantity in granular media are reviewed for slow and fast particle systems. Especially, the validity of the fluctuation-dissipation theorem in such an athermal system is explored. Experimental evidences for the fluctuation-dissipation theorem relevant effect temperature support the athermal statistical mechanics, which has been widely explored in recent years by physicists. Difficulties encountered in defining temperature or establishing thermodynamics or statistical mechanics in non-equilibrium situations are discussed.

Revisiting the Classics to Recover the Physical Sense in Electrical Noise

This paper shows a physically cogent model for electrical noise in resistors that has been obtained from Thermodynamical reasons. This new model derived from the works of Johnson and Nyquist also agrees with the Quantum model for noisy systems handled by Callen and Welton in 1951, thus unifying these two Physical viewpoints. This new model is a Complex or 2-D noise model based on an Admittance that considers both Fluctuation and Dissipation of electrical energy to excel the Real or 1-D model in use that only considers Dissipation. By the two orthogonal currents linked with a common voltage noise by an Admittance function, the new model is shown in frequency domain. Its use in time domain allows to see the pitfall behind a paradox of Statistical Mechanics about systems considered as energy-conserving and deterministic on the microscale that are dissipative and unpredictable on the macroscale and also shows how to use properly the Fluctuation-Dissipation Theorem.

Electrical Noise, Brownian Motion and the Arrow of Time

The origin of the Johnson noise of resistors is reviewed by a new model fitting in the Fluctuation-Dissipation framework and compared with the velocity noise in Brownian motion. This new model handling both fluctuations as well as dissipations of electrical energy in the Complex Admittance of any resistor excels current model based on the dissipation in their conductance. From the two orthogonal currents associated to a sinusoidal voltage in an electrical admittance, the new model that also considers the discreteness of the electrical charge shows a Cause-Effect dynamics for electrical noise. After a brief look at systems considered as energy-conserving and deterministic on the microscale that are dissipative and unpredictable on the macroscale, the arrow of time is discussed from the noise viewpoint.

On the Absence of Carrier Drift in Two-Terminal Devices and the Origin of Their Lowest Resistance Per Carrier R_k=h/Q²

After a criticism on today’s model for electrical noise in resistors, we pass to use a Quantum-compliant model based on the discreteness of electrical charge in a complex Admittance. From this new model we show that carrier drift viewed as charged particle motion in response to an electric field is unlike to occur in bulk regions of Solid-State devices where carriers react as dipoles against this field. The absence of the shot noise that charges drifting in resistors should produce and the evolution of the Phase Noise with the active power existing in the resonators of L-C oscillators, are two effects added in proof for this conduction model without carrier drift where the resistance of any two-terminal device becomes discrete and has a minimum value per carrier that is the Quantum Hall resistance Rk=h/q2

Covariant Form of Non-Markovian Langevin Equation in Phase Space

Starting from classical Lagrangian with the nonlinear system-beth interaction,a covariantform of generalized Langevin equation is derived.The transformation properties of the equation and itsquantities under a time-independent coordinate transformation in phase space are studied.

Quantum“contact”friction:The contribution of kinetic friction coefficient from thermal fluctuations

A thermal model of kinetic friction is assigned to a classical loaded particle moving on a fluctuating smooth surface.A sinusoidal wave resembles surface fluctuations with a relaxation time.The Hamiltonian is approximated to the mean energy of the wave describing a system of Harmonic oscillators.The quantization of amplitudes yields in terms of annihilation and creation operators multiplied by a quantum phase.Further,we consider acoustic dispersion relation and evaluate the friction coefficient from the force autocorrelation function.While the sliding particle remains classical describing a nano-particle or a tip with negligible quantum effects like tunneling or delocalization in the wave function,the quantized model of the surface fluctuations results in the temperature dependence of the kinetic friction coefficient.It follows an asymptotic value for higher temperatures and supper-slipperiness at low temperatures.

Improved linear response for stochastically driven systems

Abstract The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation- dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which mig：ht not be available with sufficient precision in the case of complex dynamics （usually a Gaussian approximation is used）. Here, we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response tiraes before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times.