Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Effective Action for Relativistic Hydrodynamics from the Crooks Fluctuation Theorem

A new effective theory framework for fluctuating hydrodynamics in the relativistic regime is derived using standard thermodynamical principles and general properties of nonequilibrium stochastic dynamics. For the first time, we establish clear and concise conditions for ensuring that the resulting effective theories are causal, stable, and well-posed within general relativity. Here, these properties are independent of spacetime foliation and are valid in the full nonlinear regime. Out-of-equilibrium fluctuations are constrained by a relativistically covariant version of the Crooks fluctuation theorem, which determines how the entropy production is distributed even when the system is driven by an external force. This leads to an emerging Z 2 symmetry responsible for imposing fluctuation-dissipation relations for n-point correlation functions, which matches the standard constraints for the Schwinger-Keldysh effective action.

Fluctuation theorems↗
DOE OSTI2023

Thermodynamics of signal transduction systems and fluctuation theorem in a signal cascade

Biochemical chain reactions are signal transduction cascades that can transmit biological information about the intracellular environment. In this study, we modelled a chain reaction as a code string for applying information theory. Herein, we assumed that cell signal transduction selects a strategy to maximize the transduced signal per signal event duration. To investigate the same, we calculated the information transmission capacity of the reaction chain by maximizing the average entropy production rate per reaction time, indicating the idea of the entropy coding method. Moreover, we defined a signal cascade trajectory. Subsequently, we found that the logarithm of the forward and reverse transition ratio per reaction time is equal to the entropy production rate, which derives the form of the fluctuation theorem in signal transduction. Our findings suggest the application of information entropy theory for analysing signal transduction.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Tightening the thermodynamic uncertainty relations with null-entropy events: What we learn when nothing happens

Fluctuation theorems establish that thermodynamic processes at the microscale can occasionally result in negative entropy production. At the microscale, another distinct possibility becomes more likely: processes where no entropy is produced overall. In this work, we explore the constraints imposed by such null-entropy events on the fluctuations of thermodynamic currents. By incorporating the probability of null-entropy events, we obtain tighter bounds on finite-time thermodynamic uncertainty relations derived from fluctuation theorems. We validate this framework using an example of a qudit SWAP engine.

FOS: Physical sciences↗
DOE OSTI2026

A new effective theory for stochastic relativistic hydrodynamics

Thermal fluctuations are a fundamental feature of dissipative systems that are essential for understanding physics near the expected critical point of QCD and in small systems. When such fluctuations are modeled naively in relativistic systems, strange features can appear such as negative self-correlation functions. We construct an effective theory for nonlinear stochastic relativistic hydrodynamics that ensure a well-posed mathematical formulation. Using Crooks fluctuation theorem, we derive a symmetry of the effective action that incorporates fluctuations through a suitable free energy functional. For divergence type theories, the action can then be fully specified using a single vector generating current. The equations of motion obtained using this procedure are guaranteed to be flux conservative and symmetric hyperbolic when the dynamics is causal. This ensures that these equations are well-posed (for suitable initial data) and are in a form that can easily be simulated, including with Metropolis techniques.

Mullins, Nicki [University of Illinois at Urbana-C↗
DOE OSTI2025

Mapping Local Dissipation and Entropy Production in Complex and Active Fluids

While global entropy production provides a measure of irreversibility, its partitioning into contributions from local regions is key to understanding the mechanisms underlying time-reversal symmetry breaking in complex systems and active matter. Here, by analyzing local heat flows and fluxes, we propose a framework that enables the mapping of local dissipation and entropy production in a nonequilibrium system. We test this approach in simulations of fluids driven through complex environments and active systems. We connect the results across the local and global scales by showing that local dissipation and entropy production satisfy a local version of the usual (global) fluctuation theorem, which accounts for the correlations between the local region and its surroundings. Interestingly, in the case of the active fluid, our analysis reveals that these correlations are of opposite signs for the active (stochastic) and passive (deterministic) contributions to local dissipation.

Entropy↗
DOE OSTI2025

Decoherence and Brownian motion of a polarizable particle near a medium

Optically levitated nanoparticles are ideal experimental testbeds for investigating macroscopic superpositions and microscopic thermodynamics. Integrating such levitated nanoparticles with photonic structures can enable strong coupling between their center-of-mass motion and guided photonic modes, facilitating enhanced control and probing of their motion. When coupling a particle to a photonic structure, such as a waveguide, the effects of fluctuations become prominent at nanoscales. In this work, we analyze the classical and quantized center-of-mass motion of a polarizable particle interacting with the fluctuations of the electromagnetic field in the presence of a medium. We derive a position localization master equation for the particle's quantized center of mass, and examine its classical center-of-mass momentum diffusion, elucidating correspondences between classical and quantum Brownian motion of polarizable particles near media. We study the decoherence rate of the particle in the presence of a planar surface as a function of temperature and distance from the surface, comparing it to common sources of decoherence. Our results are pertinent to experiments aimed at preparing levitated nanospheres in macroscopic quantum states and investigating their Brownian dynamics.

Brownian motion↗
DOE OSTI2024

A practical approach to calculating magnetic Johnson noise for precision measurements

Magnetic Johnson noise is an important consideration for many applications involving precision magnetometry, and its significance will only increase in the future with improvements in measurement sensitivity. The fluctuation–dissipation theorem can be utilized to derive analytic expressions for magnetic Johnson noise in certain situations, but when used in conjunction with finite element analysis tools, the combined approach is particularly powerful as it provides a practical means to calculate the magnetic Johnson noise arising from conductors of arbitrary geometry and permeability. In this paper, we demonstrate this method to be one of the most comprehensive approaches presently available to calculate thermal magnetic noise. In particular, its applicability is shown to not be limited to cases where the noise is evaluated at a point in space but also can be expanded to include cases where the magnetic field detector has a more general shape, such as a finite-size loop, a gradiometer, or a detector that consists of a polarized atomic species trapped in a volume. Furthermore, some physics insights gained through studies made using this method are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Coarse-Graining Conformational Dynamics with Multidimensional Generalized Langevin Equation: How, When, and Why

A data-driven ab initio generalized Langevin equation (AIGLE) approach is developed to learn and simulate high-dimensional, heterogeneous, coarse-grained (CG) conformational dynamics. Constrained by the fluctuation–dissipation theorem, the approach can build CG models in dynamical consistency (DC) with all-atom molecular dynamics. Here, we also propose practical criteria for AIGLE to enforce long-term DC. Case studies of a toy polymer, with 20 CG sites, and the alanine dipeptide, with two dihedral angles, elucidate why one should adopt AIGLE or its Markovian limit for modeling CG conformational dynamics in practice.

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