Abstract
Reductionism is a prevalent viewpoint in science according to which all physical phenomena can be understood from fundamental laws of physics. Anderson (Science 177:393 1972), Laughlin and Pines (PNAS 97:28 2000), and others have countered this viewpoint and argued in favour of hierarchical structure of the universe and laws. In this paper, we advance the latter perspective by showing that some of the complex flow properties—Kolmogorov’s theory of turbulence, turbulence dissipation and diffusion, and dynamic pressure—derived using hydrodynamic equations (macroscopic laws) are very difficult, if not impossible, to describe in microscopic framework, e.g. kinetic theory. We also provide several other examples of hierarchical description.
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References
Amit DJ (1978) Field theory, the renormalization group, and critical phenomena International series in pure and applied physics. World Scientific, Singapore
Anas M, Verma MK (2019) Modeling Ekman and quasi-static magnetohydrodynamic turbulence using Pao’s hypothesis. Phys Rev Fluids 4(10):104611
Anderson PW (1972) More is different. Science 177(4):393–396
Anderson PW (2011) More and different. Notes from a thoughtful Curmudgeon. World Scientific, Singapore
Auyang SY (1999) Foundations of complex-system theories: in economics, evolutionary biology, and statistical physics. Cambridge University Press, Cambridge
Balaji V (2020) Climbing down Charney’s ladder: machine learning and the post-Dennard era of computational climate science. Phill Trans.R Soc A p. preprint
Batterman RW (2002) The devil in the details. Oxford studies in philosophy of science. Oxford University Press, Oxford
Berry M (2002) Singular limits. Phys Today 55(5):10–11
Bisi M (2014) Incompressible Navier-Stokes equations from Boltzmann equations for reacting mixtures. J Phys A 47(45):455203
Bolgiano R (1959) Turbulent spectra in a stably stratified atmosphere. J Geophys Res 64(12):2226–2229
Carroll S (2011) From eternity to here. Oneworld Publications, London
Choudhuri AR (1998) The physics of fluids and plasmas: an introduction for astrophysicists. Cambridge University Press, Cambridge
Feynman RP (1963) The Feynman lectures on physics: Vol 1 mainly mechanics, radiation, and heat, 1st edn. Addison Wesley, Reading, MA
Feynman RP (1994) The character of physical law. Modern Library, New York
Fowler CMR (2004) The solid earth: an introduction to global geophysics, 2nd edn. Cambridge University Press, Cambridge
Frisch U (1995) Turbulence: the legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge
Hawking S (2006) The theory of everything. Jaico Publishing House, Mumbai
Jones CA (2008) Dynamo theory. In: Cardin P, Cugliandolo LF (eds) Dynamo. Elsevier, Amsterdam, pp 45–135
Kane G (2017) Modern elementary particle physics, 2nd edn. Cambridge University Press, Cambridge
Kolmogorov AN (1941) Dissipation of energy in locally isotropic turbulence. Dokl Acad Nauk SSSR 32:16–18
Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl Acad Nauk SSSR 30:301–305
Landau LD, Lifshitz EM (1980) Statistical physics. Course of theoretical physics, 3rd edn. Elsevier, Oxford
Landau LD, Lifshitz EM (1987) Fluid mechanics. Course of theoretical physics, 2nd edn. Elsevier, Oxford
Laughlin RB (2006) A different universe: reinventing physics from the bottom down. Basic Books, New York
Laughlin RB, Pines D (2000) The theory of everything. PNAS 97(1):28–31
Lesieur M (2008) Turbulence in fluids. Springer-Verlag, Dordrecht
Liboff RL (1998) Kinetic theory. Wiley, Hoboken
Lifshitz EM, Pitaevskii LP (2012) Physical kinetics. Course of theoretical physics. Pergamon Press, Oxford
McComb WD (1990) The physics of fluid turbulence. Clarendon Press, Oxford
Obukhov AM (1959) On influence of buoyancy forces on the structure of temperature field in a turbulent flow. Dokl Acad Nauk SSSR 125:1246
Pathria (2011) Statistical mechanics, 3rd edn. Elsevier, Oxford
Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge
Singh SK, Thantanapally C, Ansumali S (2016) Gaseous microflow modeling using the Fokker-Planck equation. Phys Rev E 94(6):063307
Siscoe GL (1983) Solar system magnetohydrodynamics. In: R.L. Carovillano, J.M. Forbes (eds.) Solar terrestrial physics principles and theoretical foundations
Succi S (2001) The lattice boltzmann equation for fluid dynamics and beyond. Clarendon Press, Oxford
Taylor GI (1954) The dispersion of matter in turbulent flow through a pipe. Proc R Soc A 223(1):446–468
Verma MK (2012) Variable enstrophy flux and energy spectrum in two-dimensional turbulence with Ekman friction. EPL 98:14003
Verma MK (2017) Anisotropy in quasi-static magnetohydrodynamic turbulence. Rep Prog Phys 80(8):087001
Verma MK (2018) Physics of buoyant flows: from instabilities to turbulence. World Scientific, Singapore
Verma MK (2019) Asymmetric energy transfers in driven nonequilibrium systems and arrow of time. Eur Phys J B 92:190
Verma MK (2019) Description of nature: A single law or many laws? Indian Acad Sci Conf Ser 2(1):121–124
Verma MK (2019) Energy transfers in fluid flows: multiscale and spectral perspectives. Cambridge University Press, Cambridge
Verma MK (2020) Boltzmann equation and hydrodynamic equations: their equilibrium and non-equilibrium behaviour. Phil Trans R Soc A 378(2175):20190470
Weinberg S (1992) Dreams of a final theory. Vintage, New York
Wilson KG, Kogut J (1974) The renormalization group and the \(\varepsilon\) expansion. Phys Rep 12(2):75–199
Zank GP, Matthaeus WH (1991) The equations of nearly incompressible fluids. I—hydrodynamics, turbulence, and waves. Phys Fluids A 3(1):69–82
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The author thanks Anurag Gupta and Michael Berry for useful discussions.
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Verma, M.K. Microscopic Laws vs. Macroscopic Laws: Perspectives from Kinetic Theory and Hydrodynamics. Trans Indian Natl. Acad. Eng. 5, 491–496 (2020). https://doi.org/10.1007/s41403-020-00152-4
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DOI: https://doi.org/10.1007/s41403-020-00152-4