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Results for “Fluctuation theorems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Electron transfer in nonpolar media

The Marcus theory of electron transfer views fluctuating orientations of permanent dipoles as the nuclear mode bringing the donor and acceptor into the tunneling resonance. Electronic polarization of the solvent is excluded as the fast mode adiabatically following the electronic density. This view, valid for solids, does not apply to molecular liquids where molecular translations (density fluctuations) modulate the induction interaction of the donor-acceptor complex with the solvent. This mechanism of promoting radiation-less electronic transitions is considered here in the framework of the perturbation liquid-state theory. The reorganization energy of electron transfer in nonpolar solvents is nonzero and reaches the values of 0.1–0.3 eV for typical molecular sizes and solvents used in applications. The reorganization energy scales quadratically with the molecular polarizability of the solvent and decays as the inverse fifth power with the size of the donor and acceptor. The combination of the entropic character of the density fluctuations, driven by re-packing of molecular cores, with the short range of induction solute–solvent interactions leads to the violation of the fluctuation–dissipation theorem for the variance of the donor-acceptor energy gap. An explicit, approximately hyperbolic, dependence of the reorganization energy on temperature is predicted. It leads to a non-Arrhenius kinetic law for the rate constant of electron transfer in nonpolar liquid solvents.

14 SOLAR ENERGY↗
DOE OSTI2020

Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: Spheres and cylinders

The structure and dynamics of confined suspensions of particles of arbitrary shape are of interest in multiple disciplines from biology to engineering. Theoretical studies are often limited by the complexity of long-range particle-particle and particle-wall forces, including many-body fluctuating hydrodynamic interactions. Here, we report a computational study on the diffusion of spherical and cylindrical particles confined in a spherical cavity. We rely on an immersed-boundary general geometry Ewald-like method to capture lubrication and long-range hydrodynamics and include appropriate non-slip conditions at the confining walls. A Chebyshev polynomial approximation is used to satisfy the fluctuation-dissipation theorem for the Brownian suspension. We explore how lubrication, long-range hydrodynamics, particle volume fraction, and shape affect the equilibrium structure and the diffusion of the particles. It is found that once the particle volume fraction is greater than 10%, the particles start to form layered aggregates that greatly influence particle dynamics. Hydrodynamic interactions strongly influence the particle diffusion by inducing spatially dependent short-time diffusion coefficients, stronger wall effects on the particle diffusion toward the walls, and a sub-diffusive regime-caused by crowding-in the long-time particle mobility. The level of asymmetry of the cylindrical particles considered here is enough to induce an orientational order in the layered structure, decreasing the diffusion rate and facilitating a transition to the crowded mobility regime at low particle concentrations. Our results offer fundamental insights into the diffusion and distribution of globular and fibrillar proteins inside cells.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Tuning nonequilibrium phase transitions with inertia

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation–dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. Further, this density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Ab initio generalized Langevin equation

We introduce a machine learning–based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori–Zwanzig formalism, under the constraint of the fluctuation–dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Adaptive nonequilibrium design of actin-based metamaterials: Fundamental and practical limits of control

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize external control or how controllable a given material can be. Here, we demonstrate that branched actin networks can be encoded with metamaterial properties by dynamically controlling the applied force under which they grow and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding “memory” within these structures. Interestingly, we obtain a bound that relates the dissipation rate and the rate of “encoding” that gives insight into the constraints on control—both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Electron-induced massive dynamics of magnetic domain walls

We study the dynamics of domain walls (DWs) in a metallic, ferromagnetic nanowire, focusing on inertial effects on the DW due to interaction with a conduction electron bath. In this work, we develop a Keldysh collective coordinate technique to describe the effect of conduction electrons on rigid magnetic structures. The effective Lagrangian and Langevin equations of motion for a DW are derived microscopically, including the full response kernel which is nonlocal in time. The DW dynamics is described by two collective degrees of freedom: position and tilt angle. The coupled Langevin equations therefore involve two correlated noise sources, leading to a generalized fluctuation-dissipation theorem (FDT). The DW response kernel due to electrons contains two parts: one related to dissipation via FDT and another reactive part. We prove that the latter term leads to a mass for both degrees of freedom, even though the intrinsic bare mass is zero. The electron-induced mass is present even in a clean system without pinning or specifically engineered potentials. The resulting equations of motion contain rich dynamical solutions and point toward a way to control domain wall motion in metals via the electronic system properties. We discuss two observable consequences of the mass, hysteresis in the DW dynamics, and resonant response to ac current.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Stochastic thermodynamic cycles of a mesoscopic thermoelectric engine

Here, we analyze a steady-state thermoelectric engine, whose working substance consists of two capacitively coupled quantum dots. One dot is tunnel-coupled to a hot reservoir serving as a heat source, the other one to two electrically biased reservoirs at a colder temperature, such that work is extracted under the form of a steady-state current against the bias. In single realizations of the dynamics of this steady-state engine autonomous, four-stroke cycles can be identified. The cycles are purely stochastic, in contrast to mechanical autonomous engines which exhibit self-oscillations. In particular, these cycles fluctuate in direction and duration and occur in competition with other spurious cycles. Using a stochastic thermodynamic approach, we quantify the cycle fluctuations and relate them to the entropy produced during individual cycles. We identify the cycle mainly responsible for the engine performance and quantify its statistics with tools from graph theory. We show that such stochastic cycles are made possible because the work extraction mechanism is itself stochastic instead of the periodic time dependence in the working-substance Hamiltonian which can be found in conventional mechanical engines. Our investigation brings new perspectives about the connection between cyclic and steady-state engines.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Langevin dynamics of generalized spins as SU( N ) coherent states

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude S have N = 2⁢S + 1 levels. Alternatively, the spin state is fully characterized by a set of N 2 - 1 local physical observables, which we interpret as generalized spin components. For example, a spin with S = 1 has three dipole components and five quadrupole components. Further, these components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of SU(N) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a nonequilibrium relaxation process that creates CP 2 skyrmions, which are topological defects with both dipole and quadrupole character.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Decoherence by warm horizons

Recently Danielson, Satishchandran, and Wald (DSW) have shown that quantum superpositions held outside of Killing horizons will decohere at a steady rate. This occurs because of the inevitable radiation of soft photons (gravitons), which imprint a electromagnetic (gravitational) “which-path” memory onto the horizon. Rather than appealing to this global description, an experimenter ought to also have a local description for the cause of decoherence. One might intuitively guess that this is just the bombardment of Hawking/Unruh radiation on the system, however simple calculations challenge this idea—the same superposition held in a finite temperature inertial laboratory does not decohere at the DSW rate. In this work we provide a local description of the decoherence by mapping the DSW setup onto a worldline-localized model resembling an Unruh-DeWitt particle detector. We present an interpretation in terms of random local forces which do not sufficiently self-average over long times. Using the Rindler horizon as a concrete example we clarify the crucial role of temperature, and show that the Unruh effect is the only quantum mechanical effect underlying these random forces. A general lesson is that for an environment which induces Ohmic friction on the central system (as one gets from the classical Abraham-Lorentz-Dirac force, in an accelerating frame) the fluctuation-dissipation theorem implies that when this environment is at finite temperature it will cause steady decoherence on the central system. Our results agree with DSW and provide the complementary local perspective. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Free-energy estimates from nonequilibrium trajectories under varying-temperature protocols

The Jarzynski equality allows the calculation of free-energy differences using values of work measured from nonequilibrium trajectories. The number of trajectories required to accurately estimate free-energy differences in this way grows sharply with the size of work fluctuations, motivating the search for protocols that perform desired transformations with minimum work. However, protocols of this nature can involve varying temperature, to which the Jarzynski equality does not apply. Here, we derive a variant of the Jarzynski equality that applies to varying-temperature protocols, and show that it can have better convergence properties than the standard version of the equality. We derive this modified equality and the associated fluctuation relation within the framework of Markovian stochastic dynamics, complementing related derivations done within the framework of Hamiltonian dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Universal energy-speed-accuracy trade-offs in driven nonequilibrium systems

The connection between measure theoretic optimal transport and dissipative nonequilibrium dynamics provides a language for quantifying nonequilibrium control costs, leading to a collection of thermodynamic speed limits, which rely on the assumption that the target probability distribution is perfectly realized. This is almost never the case in experiments or numerical simulations, so here we address the situation in which the external controller is imperfect. We obtain a lower bound for the dissipated work in generic nonequilibrium control problems that (1) is asymptotically tight and (2) matches the thermodynamic speed limit in the case of optimal driving. Along with analytically solvable examples, we refine this imperfect driving notion to systems in which the controlled degrees of freedom are slow relative to the nonequilibrium relaxation rate, and identify independent energy contributions from fast and slow degrees of freedom. Furthermore, we develop a strategy for optimizing minimally dissipative protocols based on optimal transport flow matching, a generative machine learning technique. Furthermore, this latter approach ensures the scalability of both the theoretical and computational framework we put forth. Crucially, we demonstrate that we can compute the terms in our bound numerically using efficient algorithms from the computational optimal transport literature and that the protocols we learn saturate the bound.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Time Evolution of Correlation Functions in Quantum Many-Body Systems

We give rigorous analytical results on the temporal behavior of two-point correlation functions—also known as dynamical response functions or Green’s functions—in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times $\langle$A ( t ) B$\rangle$ β → $\langle$ A$\rangle$ β $\langle$ B$\rangle$ β , thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For autocorrelation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values and does not increase with system size. We give numerical examples that show that this bound is a good estimate in nonintegrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Quantum Jarzynski Equality in Open Quantum Systems from the One-Time Measurement Scheme

In open quantum systems, a clear distinction between work and heat is often challenging, and extending the quantum Jarzynski equality to systems evolving under general quantum channels beyond unitality remains an open problem in quantum thermodynamics. In this Letter, we introduce well-defined notions of guessed quantum heat and guessed quantum work, by exploiting the one-time measurement scheme, which only requires an initial energy measurement on the system alone. We derive a modified quantum Jarzynski equality and the principle of maximum work with respect to the guessed quantum work, which requires the knowledge of the system only. We further show the significance of guessed quantum heat and work by linking them to the problem of quantum hypothesis testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Near-Field Radiative Heat Transfer Between Two α-MoO3 Biaxial Crystals

The near-field radiative heat transfer (NFRHT) between two semi-infinite α-MoO3 biaxial crystals is investigated numerically based on the fluctuation–dissipation theorem combined with the modified 4 × 4 transfer matrix method in this paper. In the calculations, the near-field radiative heat flux (NFRHF) along each of the crystalline directions of α-MoO3 is obtained by controlling the orientation of the biaxial crystals. The results show that much larger heat flux than that between two semi-infinite hexagonal boron nitride can be achieved in the near-field regime, and the maximum heat flux is along the [001] crystalline direction. The mechanisms for the large radiative heat flux are explained as due to existence of hyperbolic phonon polaritons (HPPs) inside α-MoO3 and excitation of hyperbolic surface phonon polaritons (HSPhPs) at the vacuum/α-MoO3 interfaces. The effect of relative rotation between the emitter and the receiver on the heat flux is also investigated. It is found that the heat flux varies significantly with the relative rotation angle. The modulation contrast can be as large as two when the heat flux is along the [010] direction. We attribute the large modulation contrast mainly to the misalignment of HSPhPs and HPPs between the emitter and the receiver. Hence, the results obtained in this work may provide a promising way for manipulating near-field radiative heat transfer between anisotropic materials.

Engineering↗
DOE OSTI2023

On Relative Importance of Vehicular and Structural Motions in Defining Electrolyte Transport

Molecular motions of ionic and neutral electrolyte species determine transport properties at the continuum scale. These molecular motions can be classified as vehicular (e.g., cations moving with a solvation shell of neighboring solvent molecules) and structural (e.g., cations hopping from one solvation shell to another) motions. While literature studies have described the presence, and relative importance, of each of these motions in various electrolytes, a clear link to macroscopic transport properties has not been made. We herein establish this link by using the fluctuation-dissipation theorem to develop theoretical expressions connecting the molecular displacements to Stefan-Maxwell diffusivities. To illustrate the usefulness of the proposed equations, we study LiPF 6 in propylene carbonate as an exemplar electrolyte. We show that its transport behavior improves at all concentrations when structural diffusion of cations is promoted. On the other hand, boosting the cation vehicular diffusion negatively affects the concentrated compositions. We extend this understanding to a generalized electrolyte of a salt dissolved in a solvent. Our theory suggests that while structural diffusion influences Stefan-Maxwell diffusivities globally, vehicular diffusion is only relevant under certain conditions. Such guidelines are critical for a bottom-up design of electrolyte transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗