Time-correlation functions for odd Langevin systems

TL;DR

This paper explores how odd response tensors in active Langevin systems break time-reversal symmetry in correlation functions, providing a way to estimate odd elastic constants in active materials like enzymes or motor proteins.

Contribution

It introduces the analysis of anti-symmetric parts of time-correlation functions in odd Langevin systems, revealing broken time-reversal symmetry due to odd responses.

Findings

Anti-symmetric parts of correlation functions can exist in odd Langevin systems.

These anti-symmetric parts are proportional to odd resistance or elastic constants.

Short-time asymptotics can estimate odd elastic constants in active materials.

Abstract

We investigate the statistical properties of fluctuations in active systems that are governed by non-symmetric responses. Both an underdamped Langevin system with an odd resistance tensor and an overdamped Langevin system with an odd elastic tensor are studied. For a system in thermal equilibrium, the time-correlation functions should satisfy time-reversal symmetry and the anti-symmetric parts of the correlation functions should vanish. For the odd Langevin systems, however, we find that the anti-symmetric parts of the time-correlation functions can exist and that they are proportional to either the odd resistance coefficient or the odd elastic constant. This means that the time-reversal invariance of the correlation functions is broken due to the presence of odd responses in active systems. Using the short-time asymptotic expressions of the time-correlation functions, one can estimate an odd elastic constant of an active material such as an enzyme or a motor protein.