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On some problems related to transport theories in active systems
Jeudi 10 Octobre, 16H F306
I will discuss our recent efforts on understanding transport phenomena and associated theories in active matter systems. Active systems with non-conservative forces at the microscale result in non-equilibrium steady states different in nature from those arising from spatial gradients in temperature, pressure, or chemical potential by means of boundary conditions. The latter class of problems has been of intense interest for over a century and may be addressed within a well-established non-equilibrium thermodynamics formalism that unifies a variety of transport processes, building on the seminal work of Onsager, Prigogine, de Groot, and Mazur. Active matter systems, which break time reversal symmetry at the microscale or particle level, still lack a unifying thermodynamic description for explaining emergent transport phenomena. In this talk, I will discuss our recent efforts towards thermodynamic description of active systems. I will show how different active forces at the microscale manifest at the macroscopic level using Irving-Kirkwood coarse-graining procedures [1,2]. I will elucidate the differences by considering models which are driven by convective [2] and rotary active forces [1]. I will then focus on emergent transport phenomena in non-equilibrium viscous fluids with and without internal spin. To this end, I will discuss most general linear constitutive relations using symmetries and representation theorems. Upon assuming that Onsager’s regression hypothesis applies to non-equilibrium steady states, I will derive the Green-Kubo relations, and show that that odd-viscosity requires time-reversal symmetry (TRS) breaking of the stress correlations at least in fluids without internal spin [3]. If time permits, I will discuss other surprises and applications of the principles learned from active systems to three-dimensional growth of bacterial colonies [4]. References : 1. Klymko, K., Mandal, and Mandadapu, K. K., Statistical mechanics of transport processes in active fluids : Equations of hydrodynamics, J. Che
m. Phys. 147, 194109 (2017). 2. Epstein, J. M., Klymko, K., Mandadapu K. K., Statistical mechanics of transport processes in active fluids. II. Equations of hydrodynamics for active Brownian particles, J. Chem. Phys. 150, 164111 (2019). 3. Epstein, J. M., and Mandadapu, K. K., Time reversal symmetry breaking in two-dimensional non-equilibrium viscous fluids, arXiv:1907.10041 (2019). 4. Takatori, S. C., and Mandadapu, K. K., Motility-induced buckling and glassy dynamics regulate three-dimensional transitions of bacterial monolayers (Preprint available on request) (2019).