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.

References in corpus (27)

• Non-reciprocal phase transitions
• The 2019 Motile Active Matter Roadmap
• Odd viscosity in chiral active fluids
• Odd elasticity
• Statistical mechanics of a chiral active fluid
• Odd viscosity in active matter: microscopic origin and 3D effects
• Odd Diffusivity of Chiral Random Motion
• Onsager's variational principle in active soft matter
• Topological defects in solids with odd elasticity
• Active viscoelasticity of odd materials
• Time reversal symmetry breaking and odd viscosity in active fluids: Green-Kubo and NEMD results
• Non-reciprocal response of a two-dimensional fluid with odd viscosity
• Time reversal symmetry breaking in two-dimensional non-equilibrium viscous fluids
• Dynamics of a trapped Brownian particle in shear flows
• Self-organized swimming with odd elasticity
• Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity
• Fluctuation Properties of Steady-State Langevin Systems
• Mechanochemical enzymes and protein machines as hydrodynamic force dipoles: The active dimer model
• Non-equilibrium probability flux of a thermally driven micromachine
• Synchronization and enhanced catalysis of mechanically coupled enzymes
• The Onsager-Machlup Integral for Non-reciprocal Systems with Odd Elasticity
• Nonequilibrium oscillations, probability angular momentum, and the climate system
• Odd Microswimmer
• Thermally Driven Elastic Micromachines
• Nonreciprocality of a micromachine driven by a catalytic chemical reaction
• Irreversibility and entropy production of a thermally driven micromachine
• Fluctuating, Lorentz-force-like coupling of Langevin equations and heat flux rectification

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