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.

Variational methods and deep Ritz method for active elastic solids

“…Here we are particularly interested in the physics of soft and biological matter, in which two variational principles are mostly relevant: the principle of minimum free energy for static problems 33,34 and Onsager's variational principle (or similar principles that extend Lagrangian variational mechanics to dissipative systems 35 ) for dynamic problems. 29,31,36–40 The former principle is of our particular interests in this work and is most relevant to active elastic solids.…”

“…These methods are mostly based on two variational principles of statistical thermodynamics: the variational principle of minimum free energy (MFEVP) for static problems 33,34 and Onsager's variational principle (OVP) for dynamic problems. 31,33,36,39,66,67 In our former work, 36 we have explored the variational methods that are based on OVP for the modeling of active matter dynamics. Here in this work, we have focused on the variational methods that are based on MFEVP and can be used for the modeling of static problems in active solids.…”

“…However, at time scales that are smaller than the structural relaxation time (such as unbinding time of crosslinkers in cytoskeleton and characteristic time of cell migration/division/apoptosis in connective tissues), active matter is more rigid and behaves as an elastic solid. 1,6,26–28 Whereas active fluids have been studied extensively, 2,4,29–31 active solids have received much less attention. 1,28,32…”

Odd Viscosity and Odd Elasticity

“…In References 315 and 319 the active hinge is immersed in a viscous fluid, and the limit cycle results in swimming behavior (see Figure 7f ). The interplay between nonconservative forces and noise has also been studied (320,321). In the context of the swimming hinges, it is shown that random fluctuations give rise (on average) to persistent motion (315,319).…”

Hydrodynamics of an odd active surfer in a chiral fluid

“…Odd viscosity is a rheological property that describes chiral fluids [66,67] and represents a transport coefficient that does not contribute to dissipation of mechanical energy of the fluid [68]. The effect of odd viscosity on various types of flows has been examined extensively in the context of microparticle transport [59,60,62,69] or Langevin dynamics in fluctuating active systems [70]. Although swimming in fluids with odd viscosity has been partially studied using the geometric theory of low-Reynolds-number locomotion of nearly circular microswimmers [71], to the best of our knowledge, the individual and pair dynamics of microswimmers in an odd fluid have not been addressed so far.…”