Generalized thermodynamics of motility-induced phase separation: phase equilibria, Laplace pressure, and change of ensembles

Motility-induced phase separation leads to cohesive active matter in the absence of cohesive forces. We present, extend and illustrate a recent generalized thermodynamic formalism which accounts for its binodal curve. Using this formalism, we identify both a generalized surface tension, that controls finite-size corrections to coexisting densities, and generalized forces, that can be used to construct new thermodynamic ensembles. Our framework is based on a non-equilibrium generalization of the Cahn–Hilliard equation and we discuss its application to active particles interacting either via quorum-sensing interactions or directly through pairwise forces.

[1]  C. M. Rohwer,et al.  Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory. , 2017, The Journal of chemical physics.

[2]  K. Klymko,et al.  Phase separation and large deviations of lattice active matter. , 2017, The Journal of chemical physics.

[3]  Hugues Chaté,et al.  Fore-aft asymmetric flocking. , 2017, Physical review. E.

[4]  I. Pagonabarraga,et al.  Active Brownian equation of state: metastability and phase coexistence. , 2017, Soft matter.

[5]  M. Cates,et al.  Generalized thermodynamics of phase equilibria in scalar active matter. , 2016, Physical review. E.

[6]  M. Dijkstra,et al.  Chemical potential in active systems: predicting phase equilibrium from bulk equations of state? , 2016, 1609.02773.

[7]  Julien Tailleur,et al.  How Far from Equilibrium Is Active Matter? , 2016, Physical review letters.

[8]  Caleb G. Wagner,et al.  Classical Nucleation Theory Description of Active Colloid Assembly. , 2016, Physical review letters.

[9]  R. Dickman.  Phase coexistence far from equilibrium , 2016, 1602.03507.

[10]  Giovanni Volpe,et al.  Engineering sensorial delay to control phototaxis and emergent collective behaviors , 2015, 1511.04528.

[11]  C. Maggi,et al.  Towards a statistical mechanical theory of active fluids. , 2015, Soft matter.

[12]  M. Cates,et al.  Active brownian particles and run-and-tumble particles: A comparative study , 2015, The European Physical Journal Special Topics.

[13]  J. Brader,et al.  Effective interactions in active Brownian suspensions. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Chiu Fan Lee.  Interface stability, interface fluctuations, and the Gibbs-Thomson relationship in motility-induced phase separations. , 2015, Soft matter.

[15]  M. Kardar,et al.  Pressure and phase equilibria in interacting active brownian spheres. , 2014, Physical review letters.

[16]  Jonathan T. Siebert,et al.  Negative Interfacial Tension in Phase-Separated Active Brownian Particles. , 2014, Physical review letters.

[17]  M. Kardar,et al.  Pressure is not a state function for generic active fluids , 2014, Nature Physics.

[18]  D. Marenduzzo,et al.  Motility-induced phase separation in an active dumbbell fluid , 2014 .

[19]  L. Berthier,et al.  Nonequilibrium equation of state in suspensions of active colloids , 2014, 1411.7175.

[20]  J. Brady,et al.  Towards a thermodynamics of active matter. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  J. Brady,et al.  Swim pressure: stress generation in active matter. , 2014, Physical review letters.

[22]  Michael E. Cates,et al.  Motility-Induced Phase Separation , 2014, 1406.3533.

[23]  L. Berthier,et al.  Clustering and heterogeneous dynamics in a kinetic Monte Carlo model of self-propelled hard disks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  M. Marchetti,et al.  Aggregation and segregation of confined active particles. , 2014, Soft matter.

[25]  Thomas Speck,et al.  Effective Cahn-Hilliard Equation for the Phase Separation of Active Brownian Particles , 2013, 1312.7242.

[26]  M. Cates,et al.  Scalar φ4 field theory for active-particle phase separation , 2013, Nature Communications.

[27]  M. Cates,et al.  Phase behaviour of active Brownian particles: the role of dimensionality. , 2013, Soft matter.

[28]  Holger Stark,et al.  Hydrodynamics determines collective motion and phase behavior of active colloids in quasi-two-dimensional confinement. , 2013, Physical review letters.

[29]  R. Winkler,et al.  Cooperative motion of active Brownian spheres in three-dimensional dense suspensions , 2013, 1308.6423.

[30]  T. Speck,et al.  Microscopic theory for the phase separation of self-propelled repulsive disks , 2013, 1307.4908.

[31]  Adriano Tiribocchi,et al.  Continuum theory of phase separation kinetics for active Brownian particles. , 2013, Physical review letters.

[32]  Ramin Golestanian,et al.  Run-and-tumble dynamics in a crowded environment: persistent exclusion process for swimmers. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Thomas Speck,et al.  Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles. , 2013, Physical review letters.

[34]  R. Golestanian,et al.  Hydrodynamic suppression of phase separation in active suspensions. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  J. Tailleur,et al.  When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation , 2012, 1206.1805.

[36]  C. Ybert,et al.  Dynamic clustering in active colloidal suspensions with chemical signaling. , 2012, Physical review letters.

[37]  J. Tailleur,et al.  Pattern formation in self-propelled particles with density-dependent motility. , 2012, Physical review letters.

[38]  M Cristina Marchetti,et al.  Athermal phase separation of self-propelled particles with no alignment. , 2012, Physical review letters.

[39]  T. Hwa,et al.  Sequential Establishment of Stripe Patterns in an Expanding Cell Population , 2011, Science.

[40]  M. Cates,et al.  Lattice models of nonequilibrium bacterial dynamics , 2010, 1012.0786.

[41]  Christophe Ybert,et al.  Sedimentation and effective temperature of active colloidal suspensions. , 2010, Physical review letters.

[42]  M E Cates,et al.  Statistical mechanics of interacting run-and-tumble bacteria. , 2008, Physical review letters.

[43]  E. Bertin,et al.  Intensive thermodynamic parameters in nonequilibrium systems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  E. Bertin,et al.  Definition and relevance of nonequilibrium intensive thermodynamic parameters. , 2005, Physical review letters.

[45]  C. Landim,et al.  Scaling Limits of Interacting Particle Systems , 1998 .

[46]  D. Dean.  LETTER TO THE EDITOR: Langevin equation for the density of a system of interacting Langevin processes , 1996, cond-mat/9611104.

[47]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[48]  A. Bray.  Theory of phase-ordering kinetics , 1993, cond-mat/9501089.

[49]  Kurt Binder,et al.  Theory of first-order phase transitions , 1987 .

[50]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[51]  J. Kirkwood,et al.  The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics , 1950 .