There are two related directions of work on non-equilibrium self assembly in our group.

Using the formalism of stochastic thermodynamics, we derive a set of design principles for growing controlled assemblies far from equilibrium. The design principles constrain the set of structures that can be obtained under non-equilibrium conditions and provides intuition for how equilibrium self-assembly landscapes can be modiﬁed under ﬁnite non-equilibrium drive.

Relevant publications:

M. Nguyen, S. Vaikuntanathan "Design principles for nonequilibrium self assembly",

10.1073/pnas.1609983113, 2016. [See commentary]*PNAS*-
Driving forces exerted on a liquid can lead to phase separations not encountered at equilibrium. Understanding the physics leading to such phase separations requires an understanding of non-equilibrium thermodynamics. Using simulations and theory, we study how energy dissipation changes fluctuations in the force the particles in a driven liquid feel. The change in the force fluctuations translate into a change in the diffusion of the particles. A difference in how fast the particles diffuse depending on their local environment can then be used to rationalize the phase separation. We are thus able to make a direct connection between the energy consumed by the system and the phase diagram. The renormalization of force fluctuations by driving forces may be extended to think about how forces in active nematics and other more complex non-equilibrium systems modify their material properties.

Relevant publications:

C. del Junco, L. Tociu, S. Vaikuntanathan, "Energy dissipation and fluctuations in a driven liquid", arXiv preprint arXiv:1611.00635

Biological processes at the subcellular level are inherently stochastic due to thermal fluctuations. Yet, in nature the noise associated with the outcomes of these processes - such as the duration of periods in circadian rhythms, or the number of errors in a transcribed RNA - is and must be quite low. We are interested in how biology uses energy consumption - a hallmark of living systems - to increase the accuracy and robustness of these processes. Many biological networks can be abstractly represented as master equations:

Here, P is a probability vector representing the probability of finding the system in each given state of the network, and W is a transition matrix that evolves the probabilities forward in time. Using this representation, we can apply the tools of linear algebra and stochastic simulations to understand how pushing the systems far from equilibrium affects the properties of the network, such as steady-state probabilities and relaxation times, which are contained in the eigenvalues and eigenvectors of the transition matrix.

Using such approaches, we can investigate general networks like the one pictured above, and apply the results to predict and explain behaviors in specific biological systems such as chemotaxis and switching of the flagellar motor in E. Coli.

Relevant publications:

*A. Murugan, *S. Vaikuntanathan, "Biological Implications of Dynamical Phases in Non-equilibrium Networks", [* equal contribution], ** J. Stat. Phys.**, 162, 1183-1202, 2016.

A. Murugan, S. Vaikuntanathan, "Topologically protected modes in non-equilibrium stochastic systems",

Self-organized liquid droplets of biomaterial that grow and divide are intriguing models for cell structures besides being novel instances of active matter. Recent experiments indicate spindle-shaped droplets of biomaterial that are susceptible to shape change and division under molecular motor activity. We use notions of statistical thermodynamics of soft matter to build phenomenological models of motor-droplet interactions.

Relevant publications:

K. L. Weirich, S. Banerjee, K. Dasbiswas, T. A. Witten, S. Vaikuntanathan, M. L. Gardel, "Liquid behavior of cross-linked actin bundles", ** PNAS** 10.1073/pnas.1616133114, 2017.

Topological materials are usually studied as isolated systems, and they host special modes. What happens if they are put into a bath? In collaboration with Prof. Irvine, we study behaviors of topological gyroscopic metamaterials in active baths.

Relevant publications:

We study fluids with high concentrations of ions which have interesting features such as unexpected colloidal stability and oscillatory spatial charge-charge correlations. We are particularly interested in describing how properties of these fluids can be leveraged to tune assembly processes within the fluids.

Relevant publications:

H. Zhang, K. Dasbiswas, N. B. Ludwig, G. Han, B. Lee, S. Vaikuntanathan, D. V. Talapin, "Stable colloids in molten inorganic salts", ** Nature**, 542, 328-331, 2017.