A First-Order Dynamical Transition in the displacement distribution of a Driven Run-and-Tumble Particle

We study the probability distribution $P(X_N=X,N)$ of the total displacement $X_N$ of an $N$-step run and tumble particle on a line, in presence of a constant nonzero drive $E$. While the central limit theorem predicts a standard Gaussian form for $P(X,N)$ near its peak, we show that for large positive and negative $X$, the distribution exhibits anomalous large deviation forms. For large positive $X$, the associated rate function is nonanalytic at a critical value of the scaled distance from the peak where its first derivative is discontinuous. This signals a first-order dynamical phase transition from a homogeneous `fluid' phase to a `condensed' phase that is dominated by a single large run. A similar first-order transition occurs for negative large fluctuations as well. Numerical simulations are in excellent agreement with our analytical predictions.Comment: 35 pages, 5 figures. An algebraic error in Appendix B of the previous version of the manuscript has been corrected. A new argument for the location $z_c$ of the transition is reported in Appendix B.

PENYUSUNAN BUKU PENGAYAAN PINTU GERBANG DIMENSI EKSPLANASI KELAS V DAN VI SD BAHASA INDONESIA MATERI TEKS EKSPLANASI SESUAI STANDAR PENERBIT PT INTAN PARIWARA

Enrichment book development is an important process in the context of modern education. Enrichment books are designed to provide additional material or activities that can enrich students' understanding beyond the main curriculum. This research aims to: 1). Describe the principles of developing Indonesian language enrichment books on explanatory text material for elementary school grades V and VI based on the publishing standards of PT Intan Pariwara, 2). Describe the process of preparing Indonesian language enrichment books on explanatory text material for elementary school grades V and VI. Translated with DeepL.com (free version) This research is included in qualitative research. There is also data collected using case study techniques. The data was analyzed by collecting data from documentation during PKP activities and then described by including relevant literature sources. The results of the research obtained are in the preparation of enrichment books must pay attention to the principles that apply according to the standards of the publisher PT Intan Pariwara. These principles include curriculum relevance, language, readability and understandability, appropriate level of difficulty, diversity of material, ability to develop creativity, and use of technology. By applying the existing principles, the process of preparing enrichment books will run optimally. Translated with DeepL.com (free version)