Anomalous Thermodynamics in Homogenized Generalized Langevin Systems

TL;DR

This paper investigates the limits of generalized Langevin systems and reveals that effective thermodynamic functionals often require anomalous correction terms due to symmetry breaking, impacting nonequilibrium system modeling.

Contribution

It demonstrates that in homogenized generalized Langevin systems, anomalous terms are generally needed for accurate thermodynamic functional descriptions, highlighting the role of area anomaly and symmetry breaking.

Findings

Effective functionals often need anomalous correction terms.

Symmetry breaking leads to area anomaly affecting convergence.

Results hold in a strong pathwise sense.

Abstract

We study functionals, such as heat and work, along trajectories of a class of multi-dimensional generalized Langevin systems in various limiting situations that correspond to different level of homogenization. These are the situations where one or more of the inertial time scale(s), the memory time scale(s) and the noise correlation time scale(s) of the systems are taken to zero. We find that, unless one restricts to special situations that do not break symmetry of the Onsager matrix associated with the fast dynamics, it is generally not possible to express the effective evolution of these functionals solely in terms of trajectory of the homogenized process describing the system dynamics via the widely adopted Stratonovich convention. In fact, an anomalous term is often needed for a complete description, implying that convergence of these functionals needs more information than simply the limit of the dynamical process. We trace the origin of such impossibility to area anomaly, thereby linking the symmetry breaking and area anomaly. This hold important consequences for many nonequilibrium systems that can be modeled by generalized Langevin equations. Our convergence results hold in a strong pathwise sense.