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Pressure is not a state function for generic active fluids


Pressure is the mechanical force per unit area that a confined system exerts on its container. In thermal equilibrium, it depends only on bulk properties—such as density and temperature—through an equation of state. Here we show that in a wide class of active systems the pressure depends on the precise interactions between the active particles and the confining walls. In general, therefore, active fluids have no equation of state. Their mechanical pressure exhibits anomalous properties that defy the familiar thermodynamic reasoning that holds in equilibrium. The pressure remains a function of state, however, in some specific and well-studied active models that tacitly restrict the character of the particle–wall and/or particle–particle interactions.

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Figure 1: Non-interacting self-propelled ellipses.
Figure 2: Interacting self-propelled spheres.
Figure 3: Simple test for the existence of an equation of state.
Figure 4: Anisotropic pressure.
Figure 5: Inhomogeneous pressure.


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We thank K. Keren, M. Kolodrubetz, C. Marchetti, A. Polkovnikov, J. Stenhammar, R. Wittkowski and X. Yang for discussions. This work was funded in part by EPSRC EP/J007404. M.E.C. holds a Royal Society Research Professorship. Y.K. was supported by the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation. M.K. is supported by NSF grant No. DMR-12-06323. A.B. and Y.F. acknowledge support from NSF grant DMR-1149266 and the Brandeis Center for Bioinspired Soft Materials, an NSF MRSEC, DMR-1420382. Their computational resources were provided by the NSF through XSEDE computing resources and the Brandeis HPCC. Y.K., A.P.S. and J.T. thank the Galileo Galilei Institute for Theoretical Physics for hospitality. A.B., M.E.C., Y.F., A.P.S., M.K. and J.T. thank the KITP at the University of California, Santa Barbara, where they were supported through National Science Foundation Grant NSF PHY11-25925.

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All authors participated in designing the project and performing the research. A.P.S. and Y.F. performed the numerical simulations. All authors participated in writing the paper.

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Correspondence to A. P. Solon.

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Solon, A., Fily, Y., Baskaran, A. et al. Pressure is not a state function for generic active fluids. Nature Phys 11, 673–678 (2015).

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