Time-correlation functions for odd Langevin systems

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.

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Cited by in corpus (13)

• Odd Viscosity and Odd Elasticity
• Thermodynamic Bound on the Asymmetry of Cross-Correlations
• Oscillatory force autocorrelations in equilibrium odd-diffusive systems
• Hydrodynamics of an odd active surfer in a chiral fluid
• Onsager's variational principle for nonreciprocal systems with odd elasticity
• Generalized Three-Sphere Microswimmers
• Odd elasticity of a catalytic micromachine
• Non-reciprocal Phase Separations with Non-conserved Order Parameters
• The Dance of Odd-Diffusive Particles: A Fourier Approach
• Simulations of Odd Microswimmers
• Confined active particles with spatially dependent Lorentz force: an odd twist to the "best Fokker-Planck approximation"
• Dumbbell dimer dynamics in three-dimensional chiral fluids
• Irreversibility of stochastic state transitions in Langevin systems with odd elasticity