scholarly journals Molecular machines operating on the nanoscale: from classical to quantum

2016 ◽  
Vol 7 ◽  
pp. 328-350 ◽  
Author(s):  
Igor Goychuk
Keyword(s):  
Molecular Motors ◽  
High Performance ◽  
Molecular Machines ◽  
Thermal Fluctuations ◽  
Maximum Power ◽  
Thermodynamic Efficiency ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Physical Features

The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation–dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.

scholarly journals Modelling thermal fluctuations in non-ideal fluids with the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2274-2282 ◽  
Author(s):  
M. Gross ◽  
R. Adhikari ◽  
M. E. Cates ◽  
F. Varnik
Keyword(s):  
Ideal Fluid ◽  
Lattice Boltzmann ◽  
Exact Result ◽  
Thermal Fluctuations ◽  
Ideal Gas ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Wide Range ◽  
Ideal Fluids ◽  
Boltzmann Method

Recently, we proposed a theoretical framework to include thermal fluctuations into the Lattice Boltzmann (LB) method for non-ideal fluids. Here, we apply a variant thereof to a certain class of force-based non-ideal fluid LB models. We find that ideal-gas-like noise is an exact result of the fluctuation–dissipation theorem in the hydrodynamic regime. It is shown that satisfactory equilibration of the density and fluid momentum can be obtained in a simulation over a wide range of length scales.

scholarly journals Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise

2020 ◽  
Vol 54 (2) ◽  
pp. 431-463 ◽  
Author(s):  
Di Fang ◽  
Lei Li
Keyword(s):  
Differential Equation ◽  
Langevin Equation ◽  
Numerical Approximation ◽  
Generalized Langevin Equation ◽  
Fractional Gaussian Noise ◽  
Fast Evaluation ◽  
Fractional Noise ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem

The generalized Langevin equation (GLE) is a stochastic integro-differential equation that has been used to describe the movement of microparticles with sub-diffusion phenomenon. It has been proved that with fractional Gaussian noise (fGn) mostly considered by biologists, the overdamped Generalized Langevin equation satisfying fluctuation dissipation theorem can be written as a fractional stochastic differential equation (FSDE). In this work, we present both a direct and a fast algorithm respectively for this FSDE model in order to numerically study ergodicity. The strong orders of convergence are proven for both schemes, where the role of the memory effects can be clearly observed. We verify the convergence theorems using linear forces, and then verify the convergence to Gibbs measure algebraically for the double well potentials in both 1D and 2D setups. Our work is new in numerical analysis of FSDEs and provides a useful tool for studying ergodicity. The idea can also be used for other stochastic models involving memory.

QUANTUM FLUCTUATION DISSIPATION THEOREM REVISITED: REMARKS AND CONTRADICTIONS

2012 ◽  
Vol 11 (03) ◽  
pp. 1242002 ◽  
Author(s):  
L. REGGIANI ◽  
P. SHIKTOROV ◽  
E. STARIKOV ◽  
V. GRUŽINSKIS
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Fluctuation ◽  
Zero Point ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Accepted Form

The quantum fluctuation dissipation theorem (QFDT) in the Callen–Welton [ Phys. Rev.83 (1951) 34] form is critically revisited. We show that the role of the system eigenvalues is in general not correctly accounted for by the accepted form of the QFDT. As a consequence, a series of quantum results claimed in the literature, like the presence of zero point fluctuations, the violation of the quantum regression hypothesis, the non-white spectrum of the Langevin force, etc. emerge as a consequence of an incorrect application of the theorem. In this context the case of the single harmonic oscillator is illustrated as a typical example where the accepted form of the QFDT is proven to fail.

scholarly journals Multiple sources of slow activity fluctuations in a bacterial chemosensory network

2017 ◽  
Author(s):  
R. Colin ◽  
C. Rosazza ◽  
A. Vaknin ◽  
V. Sourjik
Keyword(s):  
Thermal Fluctuations ◽  
Multiple Sources ◽  
Cellular Behavior ◽  
Fluctuation Dissipation ◽  
Equilibrium Processes ◽  
Fluctuation Dissipation Theorem ◽  
Stochastic Fluctuations ◽  
Energy Consuming ◽  
Slow Activity ◽  
Susceptibility To Noise

AbstractCellular networks are intrinsically subject to stochastic fluctuations, but analysis of the resulting noise remained largely limited to gene expression. The pathway controlling chemotaxis of Escherichia coli provides one example where posttranslational signaling noise has been deduced from cellular behavior. This noise was proposed to result from stochasticity in chemoreceptor methylation, and it is believed to enhance environment exploration by bacteria. Here we combined single-cell FRET measurements with analysis based on the fluctuation-dissipation theorem (FDT) to characterize origins of activity fluctuations within the chemotaxis pathway. We observed surprisingly large methylation-independent thermal fluctuations of receptor activity, which contribute to noise comparably to the energy-consuming methylation dynamics. Interactions between clustered receptors involved in amplification of chemotactic signals are also necessary to produce the observed large activity fluctuations. Our work thus shows that the high response sensitivity of this cellular pathway also increases its susceptibility to noise, from thermal and out-of-equilibrium processes.

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