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][37][38][39][40] The former principle is of our particular interests in this work and is most relevant to active elastic 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][27][28] Whereas active fluids have been studied extensively, 2,4,[29][30][31] active solids have received much less attention. 1,28,32 In this work, we consider static elasticity problems in active solids.…”

Odd Viscosity and Odd Elasticity

“…7G-H). The interplay between nonconservative forces and noise has also been studied (269,270). In the context of the swimming hinges, it is shown that random fluctuations give rise to (on average) persistent motion (268,212).…”

Variational methods and deep Ritz method for active elastic solids

“…Variational methods have been widely used in the physical modeling of soft matter. 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 [31,33,36,39,63,64]. In our former work [36], we have explored the variational methods that are based on OVP for the modeling of active matter dynamics.…”

“…By contrast, the formulation of phenomenological models is based upon symmetry consideration, conservation laws of mass, momentum, and angular momentum, and laws of Variational principles have been proposed in various fields of physics. 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][37][38][39][40]. The former principle is of our particular interests in this work and is most relevant to active elastic solids.…”