- Access by Xinjiang University
Simple fluid with broken time-reversal invariance
Phys. Rev. E 106, 034604 – Published 8 September, 2022
DOI: https://doi.org/10.1103/PhysRevE.106.034604
Abstract
We characterize a system of hard spheres with a simple collision rule that breaks time-reversal symmetry but conserves energy. The collisions lead to an achiral, isotropic, and homogeneous stationary state whose properties are determined in simulations and compared to an approximate theory originally developed for elastic hard spheres. In the nonequilibrium fluid state, velocities are correlated, a phenomenon known from other nonequilibrium stationary states. The correlations are long-ranged decaying like in dimensions. Such correlations are expected on general grounds far from equilibrium and had previously been observed in driven or nonstationary systems.
Physics Subject Headings (PhySH)
Article Text
References (38)
- M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
- C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).
- R. P. Behringer and B. Chakraborti, The physics of jamming for granular materials, Rep. Prog. Phys. 82, 012601 (2019).
- N. V. Brilliantov and T. Pöschel, Kinetic Theory of Granular Gases (Oxford University Press, Oxford, 2004)
- J. Machta, I. Oppenheim, and I. Procaccia, Statistical mechanics of stationary states. V. fluctuations in systems with shear flow, Phys. Rev. A 22, 2809 (1980).
- J. R. Dorfman, T. R. Kirkpatrick, and J. V. Sengers, Generic long-range correlations in molecular fluids, Annu. Rev. Phys. Chem. 45, 213 (1994).
- N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, Vol. 1 (Elsevier, Amsterdam, 1992).
- J. O'Byrne, Y. Kafri, J. Tailleur, and F. van Wijland, Time irreversibility in active matter, from micro to macro, Nat. Rev. Phys. 4, 167 (2022).
- G. L. Eyink, J. L. Lebowitz, and H. Spohn, Hydrodynamics and fluctuations outside of local equilibrium: Driven diffusive systems, J. Stat. Phys. 83, 385 (1996).
- L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim, Macroscopic fluctuation theory, Rev. Mod. Phys. 87, 593 (2015).
- T. P. C. van Noije, M. H. Ernst, and R. Brito, Ring kinetic theory for an idealized granular gas, Physica A 251, 266 (1998).
- Y. Baek, A. P. Solon, X. Xu, N. Nikola, and Y. Kafri, Generic Long-Range Interactions Between Passive Bodies in an Active Fluid, Phys. Rev. Lett. 120, 058002 (2018).
- S. Chapman and T. G. Cowling, The Mathematical of Non-Uniform Gases, 2nd ed. (Cambridge University Press, Cambridge, UK, 1952).
- D. W. Candif, W. K. Lu, and J. S. Dahler, Transport properties of polyatomic fluids, a dilute gas of perfectly rough spheres, J. Chem. Phys. 42, 3445 (1965).
- M. Huthmann and A. Zippelius, Dynamics of inelastically colliding rough spheres: Relaxation of tranlational and rotational energy, Phys. Rev. E 56, R6275 (1997).
- C. Dombrowski, L. Cisneros, S. Chatkaew, R. E. Goldstein, and J. O. Kessler, Self-Concentration and Large-Scale Coherence in Bacterial Dynamics, Phys. Rev. Lett. 93, 098103 (2004).
- A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati, F. Stefanini, and M. Viale, Scale-free correlations in starling flocks, Proc. Natl. Acad. Sci. USA 107, 11865 (2010).
- U. M. B. Marconi, N. Gnan, M. Paoluzzi, C. Maggi, and R. Di Leonrado, Velocity distribution in active particles systems, Sci. Rep. 6, 23297 (2016).
- E. Flenner, G. Szamel, and L. Berthier, The nonequilibrium glassy dynamics of self-propelled particles, Soft Matter 12, 7136 (2016).
- F. S. Crawford, A theorem on elastic collisions between ideal rigid bodies, Am. J. Phys. 57, 121 (1989).
- M. Meanwell and M. Thachuk, A general, rotating, hard sphere model applied to the transport properties of a low density gas, J. Chem. Phys. 147, 064308 (2017).
- G. H. Bryan, Report on the present state of our knowledge of thermodynamics, British Association Report, Vol. 64, pp. 64–106 (1894), https://www.biodiversitylibrary.org/item/95243#page/9/mode/1upp.65.
- Homogeneous disks with are called “disks” throughout the text to discern them from the general case.
- A. Scala, T. Voigtmann, and C. De Michele, Event-driven brownian dynamics for hard spheres, J. Chem. Phys. 126, 134109 (2007).
- J. R. Dorfman, H. van Beijeren, and T. R. Kirkpatrick, Contemporary Kinetic Theory of Matter (Cambridge University Press, Cambridge, UK, 2021).
- J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic Press, London, 1986).
- M. H. Ernst, J. R. Dorfmann, W. R. Hoegy, and J. M. J. van Leeuwen, Hard-sphere dynamics and binary-collison operators, Physica 45, 127 (1969).
- P. Resibois and J. L. Lebowitz, Approximate kinetic theory of hard sphere fluids near equilibrium: 1. Formal theoryal active fluids, J. Stat. Phys. 12, 483 (1975).
- P. Rösibois, Approximate kinetic theory of hard sphere fluids near equilibrium: 2. A quasihydrodynamic approximation for the velocity autocorrelation, J. Stat. Phys. 13, 393 (1975).
- E. Leutheusser, Dynamics of a classical hard sphere gas I: Formal theory, J. Phys. C 15, 2801 (1982).
- T. Aspelmeier, M. Huthmann, and A. Zippelius, Free cooling of particles with rotational degrees of freedom, in Granular Gases, edited by T. Pöschel and S. Luding (Springer, Berlin, 2001), pp. 31–58.
- P. C. Martin, O. Parodi, and P. S. Pershan, Unified hydrodynamic theory for crystals, liquid crystals, and normal fluids, Phys. Rev. A 6, 2401 (1972).
- M. Baus and J. L. Colot, Thermodynamics and structure of a fluid of hard rods, disks, spheres, or hyperspheres from rescaled virial expansions, Phys. Rev. A 36, 3912 (1987).
- J. M. Epstein and K. K. Mandadapu, Time-reversal symmetry breaking in two-dimensional nonequilibrium viscous fluids, Phys. Rev. E 101, 052614 (2020).
- G. Szamel and E. Flenner, Long-ranged velocity correlations in dense systems of self-propelled particles, Europhys. Lett. 133, 60002 (2021).
- J. E. Avron, Odd vicsosity, J. Stat. Phys. 92, 543 (1998).
- D. Banerjee, A. Souslov, A. G. Abanov, and V. Vitelli, Odd viscosity in chiral active fluids, Nat. Commun. 8, 1 (2017).
- B. D. Lubachevsky and F. H. Stillinger, Geometric properties of random disk packings, J. Stat. Phys. 60, 561 (1990).