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Register a new userDirect evaluation of rare events in active matter from variational path sampling
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Added by
Benjamin Kuznets-Speck
Publication date
2021
fields
Physics
and research's language is
English
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Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogues, transformations between distinct metastable states in active matter proceed through rare fluctuations, however their detailed balance violating dynamics renders these events difficult to study. Here, we present a simulation method for evaluating the rate and mechanism of rare events in generic nonequilibrium systems and apply it to study the conformational changes of a passive solute in an active fluid. The method employs a variational optimization of a control force that renders the rare event a typical one, supplying an exact estimate of its rate as a ratio of path partition functions. Using this method we find that increasing activity in the active bath can enhance the rate of conformational switching of the passive solute in a manner consistent with recent bounds from stochastic thermodynamics.
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Collective motion is often modeled within the framework of active fluids, where the constituent active particles, when interactions with other particles are switched off, perform normal diffusion at long times. However, in biology, single-particle superdiffusion and fat-tailed displacement statistics are also widespread. The collective properties of interacting systems exhibiting such anomalous diffusive dynamics, which we call active Levy matter, cannot be captured by current active fluid theories. Here, we formulate a hydrodynamic theory of active Levy matter by coarse-graining a microscopic model of aligning polar active particles that perform superdiffusion akin to Levy flights. Applying a linear stability analysis on the hydrodynamic equations at the onset of collective motion, we find that, in contrast to its conventional counterpart, the order-disorder transition can become critical. We then estimate the corresponding critical exponents by finite size scaling analysis of numerical simulations. Our work highlights the novel physics in active matter that integrates both anomalous diffusive motility and inter-particle interactions.
Anomalous diffusion, manifest as a nonlinear temporal evolution of the position mean square displacement, and/or non-Gaussian features of the position statistics, is prevalent in biological transport processes. Likewise, collective behavior is often observed to emerge spontaneously from the mutual interactions between constituent motile units in biological systems. Examples where these phenomena can be observed simultaneously have been identified in recent experiments on bird flocks, fish schools and bacterial swarms. These results pose an intriguing question, which cannot be resolved by existing theories of active matter: How is the collective motion of these systems affected by the anomalous diffusion of the constituent units? Here, we answer this question for a microscopic model of active Levy matter -- a collection of active particles that perform superdiffusion akin to a Levy flight and interact by promoting polar alignment of their orientations. We present in details the derivation of the hydrodynamic equations of motion of the model, obtain from these equations the criteria for a disordered or ordered state, and apply linear stability analysis on these states at the onset of collective motion. Our analysis reveals that the disorder-order phase transition in active Levy matter is critical, in contrast to ordinary active fluids where the phase transition is, instead, first-order. Correspondingly, we estimate the critical exponents of the transition by finite size scaling analysis and use these numerical estimates to relate our findings to known universality classes. These results highlight the novel physics exhibited by active matter integrating both anomalous diffusive single-particle motility and inter-particle interactions.
The granular Leidenfrost effect (B. Meerson et al, Phys. Rev. Lett. {bf 91}, 024301 (2003), P. Eshuis et al, Phys. Rev. Lett. {bf 95}, 258001 (2005)) is the levitation of a mass of granular matter when a wall below the grains is vibrated giving rise to a hot granular gas below the cluster. We find by simulation that for a range of parameters the system is bistable: the levitated cluster can occasionally break and give rise to two clusters and a hot granular gas above and below. We use techniques from the theory of rare events to compute the mean transition time for breaking to occur. This requires the introduction of a two-component reaction coordinate.
We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.
A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.
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