Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFluctuation-Dissipation Relations Far from Equilibrium: A Case Study
122
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Fluctuation-dissipation relations or theorems (FDTs) are fundamental for statistical physics and can be rigorously derived for equilibrium systems. Their applicability to non-equilibrium systems is, however, debated. Here, we simulate an active microrheology experiment, in which a spherical colloid is pulled with a constant external force through a fluid, creating near-equilibrium and far-from-equilibrium systems. We characterize the structural and dynamical properties of these systems, and reconstruct an effective generalized Langevin equation (GLE) for the colloid dynamics. Specifically, we test the validity of two FDTs: The first FDT relates the non-equilibrium response of a system to equilibrium correlation functions, and the second FDT relates the memory friction kernel in the GLE to the stochastic force. We find that the validity of the first FDT depends strongly on the strength of the external driving: it is fulfilled close to equilibrium and breaks down far from it. In contrast, we observe that the second FDT is always fulfilled. We provide a mathematical argument why this generally holds for memory kernels reconstructed from a deterministic Volterra equation for correlation functions, even for non-stationary non-equilibrium systems. Motivated by the Mori-Zwanzig formalism, we therefore suggest to impose an orthogonality constraint on the stochastic force, which is in fact equivalent to the validity of this Volterra equation. Such GLEs automatically satisfy the second FDT and are unique, which is desirable when using GLEs for coarse-grained modeling.
rate research
Read More
We derive a set of isometric fluctuation relations, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry. These relations are exact and should apply generally to many condensed-matter physics systems. Here, we establish these relations for magnetic systems and nematic liquid crystals in a symmetry-breaking external field, and we illustrate them on the Curie-Weiss and the $XY$ models. Our relations also have implications for spontaneous symmetry breaking, which are discussed.
We present a comprehensive study about the relationship between the way Detailed Balance is broken in non-equilibrium systems and the resulting violations of the Fluctuation-Dissipation Theorem. Starting from stochastic dynamics with both odd and even variables under Time-Reversal, we exploit the relation between entropy production and the breakdown of Detailed Balance to establish general constraints on the non-equilibrium steady-states (NESS), which relate the non-equilibrium character of the dynamics with symmetry properties of the NESS distribution. This provides a direct route to derive extended Fluctuation-Dissipation Relations, expressing the linear response function in terms of NESS correlations. Such framework provides a unified way to understand the departure from equilibrium of active systems and its linear response. We then consider two paradigmatic models of interacting self-propelled particles, namely Active Brownian Particles (ABP) and Active Ornstein-Uhlenbeck Particles (AOUP). We analyze the non-equilibrium character of these systems (also within a Markov and a Chapman-Enskog approximation) and derive extended Fluctuation-Dissipation Relations for them, clarifying which features of these active model systems are genuinely non-equilibrium.
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing to the overall fluctuations of the dynamics, representing the uncertainties in the past and in the future. A generalized Einstein relation is a consequence solely because the dynamics being stationary; and the Green-Kubo formula reflects a balance between the two mechanisms. Equilibrium with reversibility is characterized by a novel covariance symmetry.
We have investigated the validity of the fluctuation-dissipation theorem (FDT) and the applicability of the concept of effective temperature in a number of non-equilibrium soft glassy materials. Using a combination of passive and active microrheology to measure displacement fluctuations and the mechanical response function of probe particles embedded in the materials, we have directly tested the validity of the FDT. Our results show no violation of the FDT over several decades in frequency (1-10$^4$ Hz) for hard sphere colloidal glasses and colloidal glasses and gels of Laponite. We further extended the bandwidth of our measurements to lower frequencies (down to 0.1 Hz) using video microscopy to measure the displacement fluctuations, again without finding any deviations from the FDT.
By analogy with linear-response we formulate the duality and reciprocity properties of current and voltage fluctuations expressed by Nyquist relations including the intrinsic bandwidths of the respective fluctuations. For this purpose we individuate total-number and drift-velocity fluctuations of carriers inside a conductor as the microscopic sources of noise. The spectral densities at low frequency of the current and voltage fluctuations and the respective conductance and resistance are related in a mutual exclusive way to the corresponding noise-source. The macroscopic variance of current and voltage fluctuations are found to display a dual property via a plasma conductance that admits a reciprocal plasma resistance. Analogously, the microscopic noise-sources are found to obey a dual property and a reciprocity relation. The formulation is carried out in the frame of the grand canonical (for current noise) and canonical (for voltage noise) ensembles and results are derived which are valid for classical as well as for degenerate statistics including fractional exclusion statistics. The unifying theory so developed sheds new light on the microscopic interpretation of dissipation and fluctuation phenomena in conductors. In particular it is proven that, as a consequence of the Pauli principle, for Fermions non-vanishing single-carrier velocity fluctuations at zero temperature are responsible for diffusion but not for current noise, which vanishes in this limit.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
