Particle entity in the Doi-Peliti and response field formalisms. (English) Zbl 1538.82028
Summary: We introduce a procedure to test a theory for point particle entity, that is, whether said theory takes into account the discrete nature of the constituents of the system. We then identify the mechanism whereby particle entity is enforced in the context of two field-theoretic frameworks designed to incorporate the particle nature of the degrees of freedom, namely the Doi-Peliti field theory and the response field theory that derives from Dean’s equation. While the Doi-Peliti field theory encodes the particle nature at a very fundamental level that is easily revealed, demonstrating the same for Dean’s equation is more involved and results in a number of surprising diagrammatic identities. We derive those and discuss their implications. These results are particularly pertinent in the context of active matter, whose surprising and often counterintuitive phenomenology rests wholly on the particle nature of the agents and their degrees of freedom as particles.
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35Q83 | Vlasov equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
field theory; particle entity; statistical physics; Doi-Peliti formalism; response field formalismReferences:
| [1] | Nardini, C.; Fodor, E.; Tjhung, E.; van Wijland, F.; Tailleur, J.; Cates, M. E., Entropy production in field theories without time-reversal symmetry: quantifying the non-equilibrium character of active matter, Phys. Rev. X, 7 (2017) · doi:10.1103/PhysRevX.7.021007 |
| [2] | Cocconi, L.; Garcia-Millan, R.; Zhen, Z.; Buturca, B.; Pruessner, G., Entropy production in exactly solvable systems, Entropy, 22, 1252 (2020) · doi:10.3390/e22111252 |
| [3] | Garcia-Millan, R.; Pruessner, G., Run-and-tumble motion in a harmonic potential: field theory and entropy production, J. Stat. Mech. (2021) · Zbl 1539.82242 · doi:10.1088/1742-5468/ac014d |
| [4] | Busiello, D. M.; Hidalgo, J.; Maritan, A., Entropy production for coarse-grained dynamics, New J. Phys., 21 (2019) · doi:10.1088/1367-2630/ab29c0 |
| [5] | Fodor, E.; Jack, R. L.; Cates, M. E., Irreversibility and biased ensembles in active matter: insights from stochastic thermodynamics (2021) |
| [6] | Gompper, G., The 2020 motile active matter roadmap, J. Phys.: Condens. Matter, 32 (2020) · doi:10.1088/1361-648X/ab6348 |
| [7] | Soto, R.; Golestanian, R., Self-assembly of active colloidal molecules with dynamic function, Phys. Rev. E, 91 (2015) · doi:10.1103/PhysRevE.91.052304 |
| [8] | Slowman, A.; Evans, M.; Blythe, R., Jamming and attraction of interacting run-and-tumble random walkers, Phys. Rev. Lett., 116 (2016) · doi:10.1103/PhysRevLett.116.218101 |
| [9] | Le Bellac, M., Quantum and Statistical Field Theory (1991), New York: Oxford University Press, New York |
| [10] | Hohenberg, P. C.; Halperin, B. I., Theory of dynamic critical phenomena, Rev. Mod. Phys., 49, 435 (1977) · doi:10.1103/RevModPhys.49.435 |
| [11] | Täuber, U. C., Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior (2014), Cambridge: Cambridge University Press, Cambridge |
| [12] | Cardy, J.; Nazarenko, S.; Zaboronski, O. V., Reaction-diffusion processes, Non-Equilibrium Statistical Mechanics and Turbulence, pp 108-61 (2008), Cambridge: Cambridge University Press, Cambridge · Zbl 1170.82355 |
| [13] | Pruessner, G2011Lecture notes on non-equilibrium statistical mechanics |
| [14] | Martin, P. C.; Siggia, E. D.; Rose, H. A., Statistical dynamics of classical systems, Phys. Rev. A, 8, 423 (1973) · doi:10.1103/PhysRevA.8.423 |
| [15] | Janssen, H-K, On a Lagrangean for classical field dynamics and renormalization group calculations of dynamical critical properties, Z. Phys. B, 23, 377 (1976) · doi:10.1007/BF01316547 |
| [16] | de Dominicis, C., Technics of field renormalization and dynamics of critical phenomena, J. Phys. Colloq., 1, C1.247-53 (1976) |
| [17] | Hertz, J. A.; Roudi, Y.; Sollich, P., Path integral methods for the dynamics of stochastic and disordered systems, J. Phys. A: Math. Theor., 50 (2016) · Zbl 1357.82062 · doi:10.1088/1751-8121/50/3/033001 |
| [18] | Dean, D. S., Langevin equation for the density of a system of interacting Langevin processes, J. Phys. A: Math. Gen., 29, L613 (1996) · Zbl 0902.60047 · doi:10.1088/0305-4470/29/24/001 |
| [19] | Gelimson, A.; Golestanian, R., Collective dynamics of dividing chemotactic cells, Phys. Rev. Lett., 114 (2015) · doi:10.1103/PhysRevLett.114.028101 |
| [20] | Velenich, A.; Chamon, C.; Cugliandolo, L. F.; Kreimer, D., On the Brownian gas: a field theory with a Poissonian ground state, J. Phys. A: Math. Theor., 41 (2008) · Zbl 1147.82016 · doi:10.1088/1751-8113/41/23/235002 |
| [21] | Lefèvre, A.; Biroli, G., Dynamics of interacting particle systems: stochastic process and field theory, J. Stat. Mech. (2007) · doi:10.1088/1742-5468/2007/07/P07024 |
| [22] | Täuber, U. C.; Howard, M.; Vollmayr-Lee, B. P., Applications of field-theoretic renormalization group methods to reaction-diffusion problems, J. Phys. A: Math. Gen., 38, R79 (2005) · Zbl 1078.81061 · doi:10.1088/0305-4470/38/17/R01 |
| [23] | Pausch, J2019Topics in statistical mechanicsPhD ThesisImperial College |
| [24] | Honkonen, J., Ito and Stratonovich calculuses in stochastic field theory (2011) |
| [25] | Binney, J. J.; Dowrick, N. J.; Fisher, A. J.; Newman, M. E J., The Theory of Critical Phenomena (1998), Oxford: Oxford University Press, Oxford |
| [26] | van Kampen, N. G., Stochastic Processes in Physics and Chemistry (1992), Amsterdam: Elsevier Science B.V., Amsterdam |
| [27] | Comtet, L., Advanced Combinatorics: The Art of Finite and Infinite Expansions (2012), Berlin: Springer Science & Business Media, Berlin |
| [28] | Gradshteyn, I. S.; Ryzhik, I. M., Table of Integrals, Series and Products (2007), San Diego, CA: Academic, San Diego, CA · Zbl 1208.65001 |
| [29] | Garcia-Millan, R.; Pausch, J.; Walter, B.; Pruessner, G., Field-theoretic approach to the universality of branching processes, Phys. Rev. E, 98 (2018) · doi:10.1103/PhysRevE.98.062107 |
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