Measures of distinguishability between stochastic processes

Detailed balance in micro- and macrokinetics and micro-distinguishability of macro-processes

We develop a general framework for the discussion of detailed balance and analyse its microscopic background. We find that there should be two additions to the well-known $T$- or $PT$-invariance of the microscopic laws of motion: 1. Equilibrium should not spontaneously break the relevant $T$- or $PT$-symmetry. 2. The macroscopic processes should be microscopically distinguishable to guarantee persistence of detailed balance in the model reduction from micro- to macrokinetics. We briefly discuss examples of the violation of these rules and the corresponding violation of detailed balance.

Markov轨迹的随机可区分性

Stochastic Distinguishability of Markovian Trajectories

本文提出任意Markov过程轨迹KL散度的时空分解公式，规避采样难题并将其关联到转移事件与等待时间统计，为生物传感器设计和信号转导优化提供理论基础。

Convergence of macrostates under reproducible processes

I show that whenever a system undergoes a reproducible macroscopic process the mutual distinguishability of macrostates, as measured by their relative entropy, diminishes. This extends the second law which regards only ordinary entropies, and hence only the distinguishability between macrostates and one specific reference state (equidistribution). The new result holds regardless of whether the process is linear or nonlinear. Its proof hinges on the monotonicity of quantum relative entropy under arbitrary coarse grainings, even those that cannot be represented by completely positive maps.

基于群体和单细胞水平分布的细胞分裂模型可区分性研究

On distinguishability among cell-division models based on population and single-cell-level distributions

本研究发现细胞分裂模型的单细胞物理量统计特性可区分不同分裂模型与生长模式，但群体水平分布在不同模型间不可区分，且该结论经模拟与实验数据验证。

Comment on "Speed Limit for Classical Stochastic Processes"

In recent letter [Phys. Rev. Lett {\bf 121}, 070601 (2018), arXiv:1802.06554], the speed limit for classical stochastic Markov processes is considered, and a trade-off inequality between the speed of the state transformation and the entropy production is given. In this comment, a more accurate inequality will be presented.

Stochastic foundations of undulatory transport phenomena: Generalized Poisson-Kac processes - Part I Basic theory

This article introduces the notion of Generalized Poisson-Kac (GPK) processes which generalize the class of "telegrapher's noise dynamics" introduced by Marc Kac in 1974, usingPoissonian stochastic perturbations. In GPK processes the stochastic perturbation acts as a switching amongst a set of stochastic velocity vectors controlled by a Markov-chain dynamics. GPK processes possess trajectory regularity (almost everywhere) and asymptotic Kac limit, namely the convergence towards Brownian motion (and to stochastic dynamics driven by Wiener perturbations), which characterizes also the long-term/l…