Every January for the past 20 years, scientists from around the world have come to Berkeley for a unique conference. Chemists, biologists, and physicists gather to talk about topics as diverse as liquid water, biological membranes, nanoparticle assembly, and quantum spins. What do these all have in common? What brings such a diverse set of scientists, all working in seemingly disparate fields, together?
It turns out that all of these topics come under the purview of statistical mechanics, a field that deals with the behavior of systems with many interacting, changing components. The late David Chandler, former professor of chemistry at UC Berkeley, put it more poetically: “Statistical mechanics is the theory with which we analyze the behavior of natural or spontaneous fluctuations. It is the ubiquitous presence of fluctuations that makes observations interesting and worthwhile. Indeed, without such random processes, liquids would not boil, the sky would not scatter light, indeed every dynamic process in life would cease.” Take a pond, for example. Its surface might look placid, but microscopically, it is the constant motion of the molecules that comprise it—their fluctuations—which give rise to liquid water’s familiar properties. There is no single configuration of molecules that characterizes a liquid, but rather an infinitely large setof configurations characterized by a probability distribution. Obtaining and studying the properties of these distributions, and connecting them to the observed properties of matter, is the business of statistical mechanics.
Although statistical mechanics was developed as a branch of physics and chemistry and used to explain the properties of gases and other states of matter, its generality has made it a useful tool in many other fields, including biology, materials science, and even finance. Whenever one is studying a large number of things, and some property of those things is fluctuating, statistical mechanics can be useful. This could be colloids diffusing randomly in a liquid, stock prices changing, or even headbangers forming mosh pits at a heavy metal concert.
Chandler’s broad interests were the impetus for the statistical mechanics conference. Originally a spin-off of another chemistry conference at Berkeley, the “mini” Berkeley Statistical Mechanics Meeting grew over the years into a fully-fledged and much-anticipated meeting. Chandler brought together scientists from many walks of life, reflecting the variety of fields dealing with phenomena pervaded by fluctuations. In addition to his own primary field—the study of liquids—Chandler invited scientists working on biological systems, materials science, and quantum physics. Chandler was also notorious for his tough (and often even confrontational) questions and his high standards of scientific rigor. This made for lively, albeit intimidating, discussions. Chandler passed away in April 2017 after a long battle with cancer. Although he is gone, the spirit of curiosity and openness to topics from diverse fields that he fostered was alive and well at this year’s conference.
The conference kicked off on Friday evening with a brief introduction by conference organizer Phillip Geissler, a UC Berkeley professor of chemistry and a former graduate student of Chandler. Two-minute talks by graduate students and junior scientists followed this introduction. These talks served as advertisements for the subsequent poster session and have gotten quite elaborate at recent meetings. Presenters projected eye-catching images of their research and even showed videos. One student who opted not to use flashy visuals wryly noted that she was too old-fashioned for such things, garnering some sheepish laughs from the audience. The posters themselves encompassed a broad assortment of subjects, ranging from biological regulatory networks to statistical methods for determining the structure of molecules. During the poster session, there was a great deal of interaction between younger and older scientists, and among people in very different fields. My own poster was visited by scientists of all different stripes, from undergraduates to professors emeriti, and from biologists to engineers. The physical proximity of people at the session, as well as the interdisciplinary spirit of the conference, encouraged discussion between researchers working on very different topics who otherwise might never have crossed paths. After the poster session, conversations (scientific and otherwise) continued at local restaurants and bars.
On Saturday and Sunday, invited speakers gave talks. While the particular subjects of these talks, like the posters, were far-flung, they all had in common themes of probability and fluctuations. Talks with more specific shared themes were generally grouped into sessions. One such theme was that of amorphous materials. Unlike crystalline solids, where molecular constituents arrange themselves in regular spatial patterns, amorphous solids lack simple, regular spatial order. Instead, their local molecular environments are heterogeneous, much like those of liquids. This forces scientists to deal with not one single geometry, but a whole distribution of structures—making it a topic of perennial interest for statistical mechanicians. A wide distribution was apparent in these speakers’ expertise as well. These ranged from Baron Peters’s methods for interrogating catalysis in amorphous solids, to Marina Guenza’s models for studying the structure and dynamics of polymers, to Jean-Louis Barrat’s studies of defects and their flow in densely packed solids.
While amorphous materials are interesting in their own right, scientists are often concerned instead with how to go from a disordered set of components into an orderly configuration—a process known as self-assembly. Self-assembly is typified by such natural processes as the formation of membranes and vesicles from mixtures of oil, water, and surfactants. It is closely related to a traditional topic of study in statistical mechanics—phase transitions. These phenomena, exemplified by the crystallization of ice from liquid water, are striking manifestations of fluctuations in molecular arrangements. Many of the ideas developed to understand phase transitions have been adopted to study self-assembly. On the practical side, self-assembly is a topic of keen interest to materials scientists, who hope to harness it to manufacture devices like solar cells. Theory and practice were both on display at the conference. Jasna Brujic showed how her lab engineered tiny colloidal droplets to assemble into polymer-like chains. She was followed by Michael Grünwald, who used computer simulations to study the assembly of nanoparticles coated with long, organic molecules. The fluctuating interactions of these molecules dictate the geometry of the lattice into which the nanoparticles assemble. Grünwald’s talk was a crowd favorite—his engaging style, along with molecular movies and a pinch of humor, kept the audience entertained. Tom Lubensky told stories about the inverse process—how ordered mechanical lattices become unstable and collapse, which he illustrated with homemade videos of lattices made with construction toys.
It was a sign of how interdisciplinary the conference was that a session on materials self-assembly was followed by one on biological systems, and even more so that a biologist, a physicist, and an engineer all spoke in that same session. Their talks were as diverse as their backgrounds, from Ilya Levental’s studies of the fatty acid mixtures that comprise cell membranes, to Ariel Amir’s talk on the connection between cell genetic variability and population growth, to Elizabeth Read’s statistical models of epigenetics (how genes interact with and are affected by their environment). Especially striking was the variety of scales that the talks covered – from the rapid microscopic jittering of biomolecules, to gradual oscillations in the populations of species over time. The wide range of length and time scales that biology exhibits are connected by the ideas of statistical mechanics. Although biomolecules and populations are physically very different entities, their fluctuations are governed by the same laws of probability. This common mathematical framework enabled scientists working on vastly different aspects of biology to understand and engage with one another.
Ideas from statistical mechanics even find relevance in places where quantum physics rules. Classical systems obey Newton’s laws of motion. Their constituents trace out trajectories with well-defined positions and velocities—think of billiard balls rolling on a smooth surface. At finite temperatures, fluctuations arise from collisions between moving particles; at zero temperature, motion ceases. By contrast, quantum systems, like electrons in a metal, admit fluctuations even at zero temperature. This is a consequence of the celebrated Heisenberg uncertainty principle, which states that it is impossible to simultaneously measure the exact position and exact velocity of a quantum-mechanical particle. Rather than having precise values, these quantities are instead described by probability distributions. This makes the study of quantum systems amenable to the techniques of statistical mechanics.Romain Vassuer showed how statistical mechanical ideas about diffusion—which are typically applied to classical systems at high temperature, like proteins in a cell—can be used to describe the dynamics of ultra-cold quantum spins. Monika Schleier-Smith then followed up by showing how similar systems can be realized and probed experimentally. Abraham Nitzan took both thermal and quantum fluctuations into account with his studies of molecular wires—tiny junctions through which electrons are forced to flow one at a time. It was amazing to learn that, even in complex and counterintuitive quantum systems, one can learn a great deal by employing relatively simple concepts of probability.
One of statistical mechanics’ frontier areas is the study of nonequilibrium systems. At thermal equilibrium—where variables like temperature, pressure, and composition are held constant—the mathematical tools of statistical mechanics are well established. These tools can even be extended to systems which are out of, but not too far from, equilibrium, like a dye molecule in a liquid which has been struck by a laser pulse. Far out of equilibrium, though, the assumptions which underpin conventional statistical mechanics break down. Variables like temperature and pressure may vary or even be ill-defined. One of the most intriguing out-of-equilibrium scenarios is found in so-called active matter, in which individual components consume internal energy and convert it into motion. Examples include bacterial colonies and the cytoskeleton of eukaryotic cells. Because the tools to describe such systems are not yet fully established, collaboration between theory and experiment and between disparate fields with different ideas is essential.
The talks on nonequilibrium systems were representative of the diversity of perspectives necessary to build such tools. Suri Vaikuntanathan discussed theoretical models showing that membranes can adopt interesting morphologies when grown under highly non-equilibrium conditions. Vincenzo Vitelli gave a colorful talk on the theory of elastic behavior that arises when one attaches miniature motors to atoms on a lattice. He was followed by Dan Needleman, who showed experimentally how mixtures of microtubules and motor proteins (reconstituted from cells) pushing and pulling against each other can create motion much like that of a real cell. David Sivak tied theory and practice together as he explained how to use statistical mechanical theory to come up with protocols that experimentalists could use to efficiently operate molecular machines.
The final nonequilibrium talk was given by applied mathematician Hugo Touchette. He travelled all the way from South Africa to discuss large deviation theory, a mathematical framework which may provide the basis for a general theory of nonequilibrium statistical mechanics. While the framework itself is now on firm footing, applying it to realistic molecular systems is challenging and largely uncharted territory. In the past several years, a few brave research groups have embraced this challenge. David Limmer’s group here at Berkeley is one of them. The group’s recent efforts have led to some potential breakthroughs in the study of liquids driven out of thermal equilibrium. In fact, to paraphrase Hugo Touchette, “The leading research institute for large deviation theory is the UC Berkeley Department of Chemistry.” Touchette and members of Limmer’s group worked closely together over the following days, a testament to the interdisciplinary nature of statistical mechanics.
Geissler gave short closing
remarks to an audience worn out from the intensity of the conference and ready
for the annual Dim Sum party. Here, one of the most exciting events of the
conference happened: the announcement of poster prizes. As participants ate,
they tried to guess who the judges were (which is usually not too difficult)
and who would win (which is less easy to guess). As lunch was winding down, Geissler
called everyone to attention and announced the winners. Their work ranged from studies
of the biological networks underlying circadian rhythms, to the thermodynamics
and kinetics of chemical reactions in nanocrystals, to the use of large
deviation theory to study nanoscale heat flow, to computer simulations of polymer
growth. The diversity of the winning presentations reflected the diversity of
topics addressed throughout the conference.
For Chandler, the statistical mechanics
conference was one of the highlights of the year. Many of his scientific
friends and trainees returned to the conference every year. After Chandler passed
away, Geissler feared that there would be nothing to bring everyone together
anymore. His fears were assuaged, however—the group of scientists that Chandler
trained is a robust and active one, and they have formed a wide-ranging, but
close, community that continues to reconvene at Berkeley. It is this, Geissler says,
that helped make this year’s conference, by many people’s accounts, one of the
strongest. The embracing of diverse fields of research, coupled with rigorous
discussion and bold exploration of statistical mechanics’ frontiers, gives one
confidence that this field of fluctuations which Chandler championed will continue
Featured photo by Leslie Dietterick.