A gentle introduction to the non-equilibrium physics of trajectories: Theory, algorithms, and biomolecular applications

TL;DR

This paper introduces non-equilibrium physics through trajectory ensembles, emphasizing their conceptual clarity and practical utility in understanding complex systems and biomolecular processes, with a focus on algorithms and applications.

Contribution

It provides a minimal formalism for non-equilibrium physics based on trajectory ensembles, linking theory, algorithms, and biomolecular applications.

Findings

Trajectory ensembles clarify first-passage times and mechanisms.

Trajectory-based algorithms advance biomolecular studies.

The trajectory picture connects diffusion equations with physical intuition.

Abstract

Despite the importance of non-equilibrium statistical mechanics in modern physics and related fields, the topic is often omitted from undergraduate and core-graduate curricula. Key aspects of non-equilibrium physics, however, can be understood with a minimum of formalism based on a rigorous trajectory picture. The fundamental object is the ensemble of trajectories, a set of independent time-evolving systems that easily can be visualized or simulated (for protein folding, e.g.), and which can be analyzed rigorously in analogy to an ensemble of static system configurations. The trajectory picture provides a straightforward basis for understanding first-passage times, "mechanisms" in complex systems, and fundamental constraints the apparent reversibility of complex processes. Trajectories make concrete the physics underlying the diffusion and Fokker-Planck partial differential equations. Last but not least, trajectory ensembles underpin some of the most important algorithms which have provided significant advances in biomolecular studies of protein conformational and binding processes.