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Register a new userFluctuation-Dissipation Relations in the absence of Detailed Balance: formalism and applications to Active Matter
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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.
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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.
Identifying dissipation is essential for understanding the physical mechanisms underlying nonequilibrium processes. {In living systems, for example, the dissipation is directly related to the hydrolysis of fuel molecules such as adenosine triphosphate (ATP)}. Nevertheless, detecting broken time-reversal symmetry, which is the hallmark of dissipative processes, remains a challenge in the absence of observable directed motion, flows, or fluxes. Furthermore, quantifying the entropy production in a complex system requires detailed information about its dynamics and internal degrees of freedom. Here we introduce a novel approach to detect time irreversibility and estimate the entropy production from time-series measurements, even in the absence of observable currents. We apply our technique to two different physical systems, namely, a partially hidden network and a molecular motor. Our method does not require complete information about the system dynamics and thus provides a new tool for studying nonequilibrium phenomena.
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.
We re-derive the Nyquist theorem and Callen-Welton fluctuation-dissipation theorem (FDT) as a consequence of detailed balance principle applied to a harmonic oscillator. The usage of electrical notions in the beginning makes the consideration understandable for every physicists. Perhaps it is the simplest derivation of these well-known theorems in statistical physics. The classical limit is understandable as a consequence of Waterston-Herapath equipartition theorem.
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.
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