State of the Art in Stochastic Dynamics in Natural and Artificial Systems

The study of stochastic dynamics in both natural and artificial systems has seen significant advancements in recent years. This multidisciplinary field integrates insights from physics, chemistry, biology, and engineering to understand how microscopic interactions and stochastic processes lead to macroscopic behaviors and emergent phenomena. Despite the progress, many open questions remain. The aim of this workshop is to explore these advances, bringing together researchers to discuss the latest developments and future directions.

1. Anomalous Diffusion and Transport Processes Anomalous diffusion, characterized by non-linear scaling of mean squared displacement with time, and/or non-Gaussian displacement distributions, challenges traditional models of Brownian motion. Recent research has provided deeper insights into the mechanisms of anomalous diffusion in various systems, utilizing models such as fractional Brownian motion and continuous time random walks. Yet, new mechanisms for anomalous diffusion, e.g., diffusing diffusivity, continue to be discovered; and differentiating between different classes of anomalous diffusion based on single-particle trajectories remains a long-standing challenge. The workshop will provide a platform to discuss theoretical, computational, and experimental challenges and developments in anomalous diffusion and transport processes.

2. Stochastic Processes in Biology Stochasticity is intrinsic to biological systems, influencing processes from gene expression to ecological dynamics. Understanding these stochastic processes is crucial for deciphering cellular functions and organismal behaviour. Techniques like Monte Carlo simulations and stochastic differential equations have been instrumental in modeling these processes. However, there are significant challenges in linking these models to experimental data and in understanding how stochasticity interacts with deterministic biological pathways. Bridging the gap between theory, computer modeling, and experiments remains an open question to be addressed in this workshop.

3. Non-Equilibrium Statistical Mechanics Non-equilibrium statistical mechanics addresses systems far from equilibrium, where traditional thermodynamics does not apply. This field has made significant strides in understanding self-organization, pattern formation, and entropy production in driven systems. While we still await a general theoretical framework for non-equilibrium systems comparable to equilibrium thermodynamics, recent advances in non-equilibrium statistical mechanics continue to shed light on transport phenomena (regular and anomalous) and on chemical reactions (including those that occur inside living cells). A key purpose of this workshop is to facilitate the formation of novel links between non-equilibrium statistical mechanics, transport processes, and living matter.

4. Stochastic Resetting Stochastic resetting, where a system intermittently returns to a specific state, has emerged as a critical concept in various fields, including search processes, biochemical reactions, and financial models. This process fundamentally alters the dynamics and steady-state properties of systems, leading to novel behaviors and optimization strategies. Despite recent progress, the implications of stochastic resetting in more complex and interacting systems are not fully understood, and there is much to be explored regarding its applications and theoretical foundations.

5. Experimental Techniques and Innovations Cutting-edge experimental methods, such as single-molecule tracking, super-resolution microscopy, and high-throughput sequencing, provide unprecedented insights into the dynamics of complex systems. These techniques enable detailed observations and manipulations at molecular and cellular scales, facilitating a deeper understanding of complex phenomena. However, there is a continuous need for innovation in experimental techniques to address the increasing complexity and resolution required by modern research questions. The development of new methods to probe dynamic processes in real-time and in vivo remains a significant challenge.

In summary, the field of complex dynamics is marked by significant methodological advancements and interdisciplinary research. This workshop aims to build on these foundations, fostering collaboration to push the boundaries of our understanding and application of complex systems theory, computation, and experiment. By addressing open questions and challenges, we hope to inspire new research directions and innovative solutions.