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Time-correlation functions for odd Langevin systems.

Kento Yasuda¹, Kenta Ishimoto¹, Akira Kobayashi²

¹Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan.

The Journal of Chemical Physics

|September 8, 2022

Summary

This summary is machine-generated.

Active systems with nonsymmetric responses break time-reversal symmetry. Odd responses in Langevin systems lead to antisymmetric time-correlation functions, allowing estimation of odd elastic constants in active materials.

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Area of Science:

Statistical mechanics
Active matter physics
Non-equilibrium thermodynamics

Background:

Active systems exhibit fluctuations governed by response properties.
Systems in thermal equilibrium typically obey time-reversal symmetry.
Nonsymmetric responses in active systems can break equilibrium assumptions.

Purpose of the Study:

Investigate statistical properties of fluctuations in active systems with nonsymmetric responses.
Analyze underdamped and overdamped Langevin systems with odd tensors.
Determine how odd responses affect time-correlation functions and time-reversal symmetry.

Main Methods:

Studied underdamped Langevin system with an odd resistance tensor.
Analyzed overdamped Langevin system with an odd elastic tensor.
Derived short-time asymptotic expressions for time-correlation functions.

Main Results:

Antisymmetric parts of time-correlation functions can exist in odd Langevin systems.
These antisymmetric parts are proportional to the odd resistance coefficient or odd elastic constant.
Time-reversal invariance is broken by odd responses in active systems.

Conclusions:

Odd responses in active systems lead to a breakdown of time-reversal symmetry.
The presence of antisymmetric parts in correlation functions quantifies this breakdown.
Odd elastic constants of active materials like enzymes can be estimated using these findings.