Speed Limit for Classical Stochastic Processes

Algebraic probability, classical stochastic processes, and counting statistics

We study a connection between the algebraic probability and classical stochastic processes described by master equations. Introducing a definition of a state which has not been used for quantum cases, the classical stochastic processes can be reformulated in terms of the algebraic probability. This reformulation immediately gives the Doi-Peliti formalism, which has been frequently used in nonequilibrium physics. As an application of the reformulation, we give a derivation of basic equations for counting statistics, which plays an important role in nonequilibrium physics.

Non-equilibrium steady states of stochastic processes with intermittent resetting

Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols. Here, we obtain the general solution for the distribution of processes in which waiting times between reset events are drawn from an arbitrary distribution. This allows for the investigation of a broader class of much more realistic processes. As an example, our results are applied to the analysis of the efficiency of constrained random search processes.

Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes

We prove the Jarzynski relation for general stochastic processes including non-Markovian systems with memory. The only requirement for our proof is the existence of a stationary state, therefore excluding non-ergodic systems. We then show how the concepts of stochastic thermodynamics can be used to prove further exact non-equilibrium relations like the Crooks relation and the fluctuation theorem on entropy production for non-Markovian dynamics.

随机学习动力学中信息获取的速度极限

Speed Limit for Information Acquisition in Stochastic Learning Dynamics

本研究将SGD建模为马尔可夫过程，推导Fisher信息流速度极限，量化信息获取速率，并在线性回归中验证其预测能力。

Color-Swap models and other stochastic processes for nongrowing scale-free networks

This paper has been withdrawn.

Method for generating two coupled Gaussian stochastic processes

Most processes in nature are coupled; however, extensive null models for generating such processes still lacks. We present a new method to generate two coupled Gaussian stochastic processes with arbitrary correlation functions. This method is developed by modifying the Fourier filtering method. The robustness of this method is proved by generating two coupled fractional Brownian motions and extending its range of application to Gaussian random fields.

String Method for Generalized Gradient Flows: Computation of Rare Events in Reversible Stochastic Processes

Rare transitions in stochastic processes can often be rigorously described via an underlying large deviation principle. Recent breakthroughs in the classification of reversible stochastic processes as gradient flows have led to a connection of large deviation principles to a generalized gradient structure. Here, we show that, as a consequence, metastable transitions in these reversible processes can be interpreted as heteroclinic orbits of the generalized gradient flow. This in turn suggests a numerical algorithm to compute the transition trajectories in configuration space efficiently, based …

Time Series Path Integral Expansions for Stochastic Processes

A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range of stochastic processes. Birth-death processes with linear rates are analysed via coherent state Doi-Peliti techniques. The $\mathfrak{su}(1,1)$ Lie algebra is utilised to capture quadratic rate birth-death processes. The techniques are also adapted to diffusion processes. All methods rely on finding a suitable reproducing kernel associated with the underlying algebra to perform the expansion. The resulting series differ from those found in standard Dyson …