Following its inception in the mid-19th century, our understanding of thermodynamic entropy has undergone many revisions, most notably through the development of microscopic descriptions by Boltzmann and Gibbs, which led to a deep understanding of equilibrium thermodynamics. The role of entropy has since moved beyond the traditional boundaries of equilibrium thermodynamics, towards problems for which the development of a statistical mechanical theory seems plausible but the a-priori probabilities of states are not known, making the definition and calculation of entropy-like quantities challenging. In this talk, we will discuss two new classes of methods that enable these computations: one based on pattern matching ideas from information theory, and the other based on basin volume calculations. These approaches provide us with very general frameworks for computing entropy, density of states, and entropy production in systems far from equilibrium. We will discuss applications of these ideas to a variety of contexts: from granular systems, to absorbing-state models, to active matter, in simulations and in experiments. Throughout the talk, I will highlight challenges and promising future directions for these measurements.

The earliest stages of planetary assembly occur in a protoplanetary disk, the cloud of dust and gas that orbits a young star. The building blocks of planets are assembled in this disk, as dust grains collide and grow, and concentrate in regions to form planetesimals. Throughout this process, the disk itself evolves dynamically, driving mass onto the star as part of the final stages of pre-main sequence growth, while also expanding in size due to angular momentum conservation. All of these processes combine to change the physical environments present in the disk, from temperature and density to the flux of ultraviolet photons, which in turn leads to constantly changing chemistry. In this talk, I will discuss how we are investigating the complex feedbacks that exist between these processes, and what they are telling us about how planetary properties are set, both in our Solar System and around other stars.

Lyotropic chromonic liquid crystal (LCLC) solutions in the nematic phase have peculiar properties. They are tumbling materials, which means that flows can easily destabilize the director alignment, and they possess a large elastic anisotropy where twist elastic deformations are energetically much cheaper than splay or bend deformations. We show how these characteristics can be exploited to induce controlled growth morphology transitions from the generic dense-branching growth to dendritic growth in the viscous- fingering instability, and how they lead to unique structure formation as the LCLC solutions are driven out-of-equilibrium by a pressure-driven flow in a microfluidic channel. In particular, we report the surprising emergence of chiral domains despite the achiral nature of the material. The chirality results from a periodic double-twist deformation of the liquid crystal and leads to striking stripe patterns vertical to the flow direction. We discuss the mechanism of this unique pathway to spontaneous mirror symmetry breaking and rationalize the selection of a well-defined period of the chiral domains.

A beautiful example of spontaneous pattern formation occurs in certain dryland environments around the globe. Stripes of vegetation alternate with stripes of bare soil, with striking regularity and on a scale readily monitored via satellites. Positive feedbacks, between infiltration of water into the soil and the vegetation itself, help concentrate this essential, but limited, resource into the vegetated zones. These feedbacks play out on the short timescales of the rare and unpredictable rainstorms that sustain life in these dry regions. In contrast, the vegetation may change very little over decades, aside from a gradual upslope colonization. In this talk I will tell you a little bit about the empirical data, the models, their analysis and the results of numerical simulations, focusing on the basic question of what sets the spacing of the vegetation bands. Our work suggests some new questions about how these fragile ecosystems might respond to changes in precipitation characteristics, such as storm strength, frequency, and seasonality, all of which are occurring as a consequence of climate change.

When we attend a demanding task, our performance is poor at low arousal (drowsy) or high arousal (anxious), but we achieve optimal performance at intermediate arousal, yielding the celebrated Yerkes-Dodson inverted-U law. Despite decades of investigations, the neural mechanisms underlying this inverted-U law are unknown. In this talk, I will elucidate the behavioral and neural mechanisms linking arousal and performance. I will show that mice during auditory and visual decision-making express an array of discrete strategies, including optimal, suboptimal and disengaged, as revealed by an HMM analysis. The optimal strategy occurs at intermediate arousal levels, measured by pupil size, consistent with the inverted-U law. Using neuropixels recordings from neural populations in the auditory cortex, we show that sound encoding is optimal at intermediate arousal level, suggesting that performance modulations occur as early as primary sensory cortex. To explain the computational principle underlying this inverted-U law, we show that in a recurrent network with E/I populations arousal induces a phase transition from a multi-attractor to a single attractor phase, and performance is optimized near the critical region. The model further predicts a monotonic decrease in neural variability induced by arousal, which we confirmed in the empirical data. Our results establish a biologically plausible theory of optimal performance based on phase transitions in attractor networks with E/I balance, whose implications for brain-inspired AI models will be briefly outlined.

Flocks of birds and schools of fish are delightful and awe-inspiring examples of collective motion that we see in nature, where groups of individuals, each possessing only limited, local information, nevertheless come together and display coordinated motion. This phenomenon also extends to much smaller scales, as in migrating clusters of cells that mediate physiological processes such as embryonic development, wound healing, and cancer metastasis. The collective, co-ordinated motion of cells allows for emergent behaviors unavailable to single cells that are critical for proper function. In this talk, I shall describe our work on modeling such phenomena in cancer cell clusters, highlighting how frustration can arise at the group level because of heterogeneity in behavior among individual cells in the cluster. I shall show how this frustration can be resolved leading to new collective phases of motion that are experimentally observed in malignant lymphocyte clusters and functionally important – enabling robust chemotaxis and “load sharing” among cells.

With conventional digital computing technology reaching its limits, there has been a renaissance in analog computing across a wide range of physical substrates. In this talk, I will introduce the concept of Physical Neural Networks [1] and describe a method my group has developed to train any complex physical system to perform as a neural network for machine-learning tasks. We have tested our method experimentally with three different systems – one mechanical, one electronic, and one photonic – and have been able to show MNIST handwritten-digit classification using each of these systems, despite the fact that none of the systems were initially designed to do machine learning.

I will describe several possible future research directions on Physical Neural Networks, including the potential to create large-scale photonic accelerators for server-side machine learning [2], smart sensors that pre-process acoustic, microwave or optical [3] signals in their native domain before digitization, new kinds of quantum neural network that don't require a carefully engineered quantum computer, and generally the prospect to endow analog physical systems with new, unexpected functionality.

[1] L.G. Wright*, T. Onodera* et al. Nature 601, 549-555 (2022)

[2] T. Wang et al. Nature Communications 13, 123 (2022)

[3] T. Wang*, M. Sohoni* et al. arXiv:2207.14293, to appear in Nature Photonics (2023)

I will review the complex phenomena displayed by one of the simplest physical systems one can think of: Three identical masses connected to each other by three harmonic springs on a frictionless plane. This system conserves angular momentum, yet can persistently rotate with zero total angular momentum. It has a well-understood regular harmonic oscillatory limit but can also show fully chaotic behavior. When combined together these two phenomena give rise to a rotational random walk with fractional exponents determined by a single parameter; the total energy of the system. We will show how the notions of Arnold diffusion, geometric phases and classical gauge field naturally arise, and how they can be intuitively understood in this simple system. No prior knowledge will be assumed.