scholarly journals Mapping current and activity fluctuations in exclusion processes: consequences and open questions

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Matthieu Vanicat ◽  
Eric Bertin ◽  
Vivien Lecomte ◽  
Eric Ragoucy
Keyword(s):  
Large Deviations ◽  
Scaling Limit ◽  
Exclusion Process ◽  
Source Model ◽  
Quantum Spin ◽  
Exclusion Processes ◽  
Dynamical Phase Transition ◽  
Markov Matrix ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar--Parisi--Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114, 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.

Physical mechanisms in impacts of interaction factors on totally asymmetric simple exclusion processes

2019 ◽  
Vol 33 (20) ◽  
pp. 1950217 ◽  
Author(s):  
Yu-Qing Wang ◽  
Jia-Wei Wang ◽  
Bing-Hong Wang
Keyword(s):  
Stochastic Dynamics ◽  
Exclusion Process ◽  
Characteristic Parameter ◽  
Exclusion Processes ◽  
Physical Mechanisms ◽  
Interaction Factor ◽  
Interaction Factors ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
The Impact

Exclusion processes are hot study issues in statistical physics and corresponding complex systems. Among fruitful exclusion processes, totally asymmetric simple exclusion process (namely, TASEP) attracts much attention due to its insight physical mechanisms in understanding such nonequilibrium dynamical processes. However, interactions among isolated TASEP are the core of controlling the dynamics of multiple TASEPs that are composed of a certain amount of isolated one-dimensional TASEP. Different from previous researches, the interaction factor is focused on the critical characteristic parameter used to depict the interaction intensity of these components of TASEPs. In this paper, a much weaker constraint condition [Formula: see text] is derived as the analytical expression of interaction factor. Self-propelled particles in the subsystem [Formula: see text] of multiple TASEPs can perform hopping forward at [Formula: see text], moving into the target site of the (i − 1)th TASEP channel at [Formula: see text] or updating into the (i + 1)th TASEP channel at [Formula: see text]. The comparison of this proposed interaction factor and other previous factors is performed by investigating the computational efficiency of obtaining analytical solutions and simulation ones of order parameters of the proposed TASEP system. Obtained exact solutions are observed to match well with Monte Carlo simulations. This research attempts to have a more comprehensive interpretation of physical mechanisms in the impact of interaction factors on TASEPs, especially corresponding to stochastic dynamics of self-propelled particles in such complex statistical dynamical systems.

scholarly journals Combinatorics of the 2-Species Exclusion Processes, Marked Laguerre Histories, and Partially Signed Permutations

10.37236/8910 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Sylvie Corteel ◽  
Arthur Nunge
Keyword(s):  
Exclusion Process ◽  
Point Of View ◽  
Asymmetric Simple Exclusion Process ◽  
Exclusion Processes ◽  
Signed Permutations ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

Starting from the two-species partially asymmetric simple exclusion process, we study a subclass of signed permutations, the partially signed permutations, using the combinatorics of Laguerre histories. From this physical and bijective point of view, we obtain a natural descent statistic on partially signed permutations; as well as partially signed permutations patterns.

Phase transitions in coupled exclusion processes constituted by TASEP and two-lane SEPs

2014 ◽  
Vol 28 (08) ◽  
pp. 1450064 ◽  
Author(s):  
Yu-Qing Wang ◽  
Rui Jiang ◽  
Qing-Song Wu ◽  
Hai-Yi Wu
Keyword(s):  
Particle Density ◽  
Mean Field ◽  
Exclusion Process ◽  
Field Analysis ◽  
Exclusion Processes ◽  
Density Profiles ◽  
One Dimensional ◽  
Asymmetric Simple Exclusion ◽  
Splitting Parameter ◽  
Simple Exclusion

This paper studies the periodic one-dimensional exclusion processes constituted by totally asymmetric simple exclusion process (TASEP) and two-lane simple exclusion processes (SEP). TASEP and SEP compete with each other. Complemented by Monte Carlo simulations, mean-field analysis has been performed. Varying current splitting parameter θ, diffusivity rate D1 (or D2) and the global particle density np, we have studied phase diagrams, typical density profiles and current diagrams.

scholarly journals Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process

2020 ◽  
Author(s):  
Eunghyun Lee ◽  
Keyword(s):  
Transition Probabilities ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Initial State ◽  
Exclusion Processes ◽  
Final State ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

We find the formulas of the transition probabilities of the N-particle multi-species asymmetric simple exclusion processes (ASEP), and show that the transition probabilities are written as a determinant when the order of particles in the final state is the same as the order of particles in the initial state.

scholarly journals Mapping TASEP back in time

2021 ◽  
Author(s):  
Leonid Petrov ◽  
Axel Saenz
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
Exclusion Process ◽  
Discrete Space ◽  
Baxter Equation ◽  
Simple Exclusion Process ◽  
Open Questions ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Hammersley Process

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

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