宏观涨落理论与大偏差诱导的GENERIC框架之比较

边界驱动零范围过程在图上的电流波动：微观与宏观方法及非可逆电阻网络理论

Current fluctuations for the boundary-driven zero-range process on graphs: microscopic versus macroscopic approach and a theory of non-reversible resistor-like networks

本文通过变分方法推导了图上电流的率泛函，揭示了微观与宏观视角的联系，并提出了一种非可逆电阻网络的简化方法。

Quantum Fluctuations and Large Deviation Principle for Microscopic Currents of Free Fermions in Disordered Media

We contribute an extension of large-deviation results obtained in [N.J.B. Aza, J.-B. Bru, W. de Siqueira Pedra, A. Ratsimanetrimanana, J. Math. Pures Appl. 125 (2019) 209] on conductivity theory at atomic scale of free lattice fermions in disordered media. Disorder is modeled by (i) a random external potential, like in the celebrated Anderson model, and (ii) a nearest-neighbor hopping term with random complex-valued amplitudes. In accordance with experimental observations, via the large deviation formalism, our previous paper showed in this case that quantum uncertainty of microscopic electric…

Action minimization and macroscopic interface motion under forced displacement

We study an one dimensional model where an interface is the stationary solution of a mesoscopic non local evolution equation which has been derived by a microscopic stochastic spin system. Deviations from this evolution equation can be quantified by obtaining the large deviations cost functional from the underlying stochastic process. For such a functional, derived in a companion paper, we investigate the optimal way for a macroscopic interface to move from an initial to a final position distant by R within fixed time T. We find that for small values of R/T the interface moves with a constant …

Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process

We present the first exact solution for the time dependent equations of the macroscopic fluctuation theory (MFT) for the symmetric simple exclusion process by combining a generalization of the canonical Cole-Hopf transformation with the inverse scattering method. For the step initial condition with two densities, the associated Riemann-Hilbert problem is solved to determine exactly the optimal density profile and the response field which produce a required fluctuation, both at initial and final times. The large deviation function of the current is derived and coincides with the formula obtaine…

几何热力学的宏观Kaehler度量与事件流形上的微观度量：CV流形上的精确配分函数。扩展Souriau温度和自发磁化

The macroscopic Kaehler metric of Geometric Thermodynamics versus the microscopic one on the Event Manifold: Exact Partition Functions on CV manifolds. Extended Souriau temperatures and spontaneous magnetizations

本文阐明了几何热力学与基于Fisher矩阵的信息几何之间的关系，首次在热力学变量的宏观接触流形上引入Kähler度量，并通过CV流形上的精确配分函数积分和Killing矩映射的非线性Casimir函数，推广了Souriau热力学，类比于铁磁自发磁化。

Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory

We introduce a multi-species generalization of the symmetric simple exclusion process with open boundaries. This model possesses the property of being integrable and appears as physically relevant because the boundary conditions can be interpreted as the interaction with particles reservoirs with fixed densities of each species. The system is driven out-of-equilibrium by these reservoirs. The steady state is analytically computed in a matrix product form. This algebraic structure allows us to obtain exact expressions for the mean particle currents and for the one and two-point correlation func…

梯度流之外的变分结构：宏观涨落理论视角

Variational structures beyond gradient flows: a macroscopic fluctuation-theory perspective

本研究从宏观涨落理论出发，通过引入通量拓展密度描述，构建抽象框架将变分结构从满足细致平衡的耗散系统推广至更广泛的随机粒子系统，给出分量分解与广义正交关系，并验证了理论的适用性。

Large deviations, dynamics and phase transitions in large stochastic heterogeneous neural networks

We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation principle, and converge towards a self-consistent non-Markovian process. The proof differs in that we are working in infinite-dimensional spaces (interaction delays), non-centered interactions and multiple cell types. The limit equation is qualitatively analyzed, and we identify a number of phase transitions in such systems upon changes in delays, connectivity p…

Gamma Convergence Approach For The Large Deviations Of The Density In Systems Of Interacting Diffusion Processes

We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow variable from the time scale of the fast variable. Its atypical behavior is encapsulated in a large N Large Deviation Principle (LDP) with a rate functional. We study the $Γ$-convergence of as $\rightarrow$ 0 and show it converges to the rate functional appearing in the Macroscopic Fluctuations Theory (MFT) for diffusive systems.

量子非平衡稳态中宏观观测量的涨落

On the Fluctuations of Macroscopic Observables in Quantum Nonequilibrium Steady States

在热力学极限下，严格研究了处于非平衡稳态的量子系统中宏观观测量的涨落。特别地，我们考虑了由两个不同温度的无限储存库耦合在一个有界区域内的量子自旋系统的非平衡稳态。在对涨落的相互作用和渐近性作适当的假设下，利用集团展开法证明了观测量经验平均的NESS期望值涨落的非平衡中心极限定理，并证明了相应的矩母函数在原点附近的解析性.通过建立相应的矩母函数的存在性和可微性，证明了一类可观量的大偏差原理。

Gradient and Generic systems in the space of fluxes, applied to reacting particle systems

In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or Gen…

超音速量子输运的宏观抑制

Macroscopic suppression of supersonic quantum transport

本文针对强相互作用量子晶格气体，证明宏观粒子团簇的超音速输运概率受指数抑制，抑制强度随系统规模增大，建立了普适的动力学大偏差原理（MASSMAT）。

离散和连续Muttalib-Borodin过程：大偏差和极限形状分析

Discrete and Continuous Muttalib--Borodin Process: Large Deviations and Limit Shape Analysis

本文研究了根据q^Volume加权Muttalib-Borodin族分布的平面分割的渐进行为，建立了过程的大偏差原理，推导了极限形状的闭式公式，并揭示了平衡测度在硬边处的连续变化指数。