Fluctuation theorems and 1/f noise from a simple matrix

Chamberlin, Ralph V.; Abe, Sumiyoshi; Davis, Bryce F.; Greenwood, Priscilla E.; Shevchuk, Andrew S. H.

doi:10.1140/epjb/e2016-70242-0

Cited by 5 publications

(11 citation statements)

References 35 publications

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“…same X, N, or E), mimicking the statistics of indistinguishable particles. In previous work it has been shown that removing the alignment degeneracy from systems with the same X yields 1/f-like noise, with several features that match the low-frequency fluctuations measured in metal films and tunnel junctions [17,[74][75][76]. Here we describe how removing the energy degeneracy from systems with the same E yields similar 1/f-like noise at lower frequencies, combined with Johnson-Nyquist-like (white) noise at higher frequencies.…”

Section: Entropy and Heat In An Ideal 1-d Polymersupporting

confidence: 55%

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Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior

Chamberlin¹,

Clark²,

Mújica³

et al. 2021

Preprint

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Here we investigate how the local properties of particles in a thermal bath may influence the thermodynamics of the bath, and consequently alter the statistical mechanics of subsystems that comprise the bath. We are guided by the theory of small-system thermodynamics, which is based on two primary postulates: that small systems can be treated self-consistently by coupling them to an ensemble of similarly small systems, and that a large ensemble of small systems forms its own thermodynamic bath. We adapt this “nanothermodynamics” to investigate how a large system may subdivide into an ensemble of smaller subsystems, causing internal heterogeneity across multiple size scales. For the semi-classical ideal gas, maximum entropy favors subdividing a large system of “atoms” into an ensemble of “regions” of variable size. The mechanism of region formation could come from quantum exchange symmetry that makes atoms in each region indistinguishable, while decoherence between regions allows atoms in separate regions to be distinguishable by their distinct locations. Combining regions reduces the total entropy, as expected when distinguishable particles become indistinguishable, and as required by a theorem in quantum mechanics for sub-additive entropy. Combining large volumes of small regions gives the usual entropy of mixing for a semi-classical ideal gas, resolving Gibbs paradox without invoking quantum symmetry for atoms that may be meters apart. Other models presented here are based on Ising-like spins, which are solved analytically in one dimension. Focusing on the bonds between the Ising-like spins we find similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for fully-accurate predictions. Another result using Ising-like spins involves simulations that include a nonlinear correction to Boltzmann’s factor, which mimics the statistics of indistinguishable states by imitating the dynamics of spin exchange on intermediate lengths. These simulations exhibit 1/f-like noise at low frequencies (f), and white noise at higher f, similar to equilibrium thermal fluctuations found in many materials.

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Section: Entropy and Heat In An Ideal 1-d Polymersupporting

confidence: 55%

“…We now expand on the concept of local heat baths in nanothermodynamics [35,74] to show how Eq. (19) facilitates reversible fluctuations.…”

Section: Entropy and Heat In An Ideal 1-d Polymermentioning

confidence: 99%

Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior

Chamberlin¹,

Clark²,

Mújica³

et al. 2021

Preprint

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“…More importantly, various experimental techniques have shown that the localization is associated with abrupt decorrelation across sharp boundaries between neighboring regions in the measurements [67][68][69], unlike the strong correlations between neighboring blocks in MD simulations. In fact, we suggest that models with interactions that facilitate this decorrelation can improve the agreement between MD simulations, theory, and measured thermal and dynamic properties of real materials, as has been done for MC simulations [28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 80%

“…Furthermore, this correction significantly improves agreement between MC simulations of standard models and the measured response of many materials, including critical fluids and ferromagnets [29,30]. Moreover, a related correction provides a common foundation for 1/f noise found at low frequencies in most substances [31][32][33].…”

Section: Introductionmentioning

confidence: 84%

“…Indeed, a quadratic correction to Boltzmann's factor in the Metropolis algorithm for MC simulations alters the pe fluctuations so that they are consistent with entropy that is extensive and additive [28]. Furthermore, this correction significantly improves agreement between MC simulations of standard models and the measured response of many materials, including critical fluids and ferromagnets [29][30][31][32][33]. Future work will be necessary to determine whether the failure of the EFR for MD simulations may also be treated by a nonlinear correction from the local entropy, without having to include explicit information from surrounding parts of the sample.…”

Section: A) Anomalous Pe Fluctuations Come From Localized Energymentioning

confidence: 99%

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Energy localization and excess fluctuations from long-range interactions in equilibrium molecular dynamics

Chamberlin

Mújica

Izvekov

et al. 2020

Physica A: Statistical Mechanics and its Applications

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Molecular dynamics (MD) simulations of standard systems of interacting particles ("atoms") give excellent agreement with the equipartition theorem for the average energy, but we find that these simulations exhibit finite-size effects in the dynamics that cause local fluctuations in energy to deviate significantly from the analogous energy fluctuation relation (EFR). We have made a detailed analysis of Lennard-Jones atoms to track the origin of such unphysical fluctuations, which must be corrected for an appropriate description of the statistical mechanics of small systems, especially at low temperatures (T). Similar behavior is found in a model of nitromethane at higher T. The main conclusion of our study is that systems separated into nanometer-sized "blocks" inside much larger simulations exhibit excess fluctuations in potential energy (pe) that diverge inversely proportional to T in a manner that is strongly dependent on the range of interaction. Specifically, at low T with long-range interactions pe fluctuations exceed the EFR by at least an order of magnitude, dropping abruptly to below the EFR when interactions include only 1 st -neighbor atoms. Thus, excess pe fluctuations cannot be due to simple surface effects from the robustly harmonic 1 stneighbor interactions, nor from any details in the simulations or analysis. A simplistic model that includes 2 nd -neighbor interactions matches the excess fluctuations, but only if the 2 nd -neighbor energy is not included in Boltzmann's factor, attributable to anharmonic effects and energy localization. Empirically, adding 2 ndneighbor interactions considerably increases the width of the pe distribution, suggesting that Anderson localization may play a role. Characterizing energy correlations as a function of time and distance reveals that excess pe fluctuations in each block coincide with negative pe correlations between neighboring blocks, whereas reduced pe fluctuations coincide with positive pe correlations. Indeed, anomalous pe fluctuations in small systems can be quantified using a net local energy in Boltzmann's factor that includes pe from the surrounding shell of similarly small systems, or equivalently an effective local temperature. Our results and analysis elucidate the source of non-Boltzmann fluctuations, and the need to include mesoscopic thermal effects from the local environment for a consistent theoretical description of the equilibrium fluctuations in MD simulations of standard models with long-range interactions.

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