Fall/Winter 2022 Alumni Magazine

Developing A General Non-Equilibrium Theoretical Framework

By Zhiyue Lu

Energy and information are probably the two most crucial quantities to describe the vivid world evolving around us. Energy characterizes the potential of one system to alter another system. Energy gives one the ability to generate motion, separate and enrich materials, exchange heat, and drive chemical reactions. Information, then, characterizes the inherent statistical correlation between distinct systems. For example, a living organism can increase its chance of survival by obtaining information, which is characterized by the correlation between the organism’s living strategy with the current (or even the future trend of) environmental conditions. The flow between energy and information constitute a critical a pillar to almost any process in the world.

Despite the success of thermodynamics theory and the trending studies of information thermodynamics, energy flow, and information flow can still only be well described for processes limited to near-equilibrium or at non-equilibrium steady states. However, most of the interesting chemical processes and living organisms operate at a distance from equilibrium. Can there be a general non-equilibrium theoretical framework to describe, predict and even guide the design of the energy and information flows for complex systems far from equilibrium? This is the question that guides thermodynamics study within the Lu group.

The Lu group has made a number of baby steps (but important steps) made toward the long-term goal of developing a general non-equilibrium theoretical framework. By constructing toy models and performing numerical simulations and mathematical derivations, researchers at the Lu group are actively identifying the universal principles behind non-equilibrium energy and information flows within several types of complex systems, examples of which are on the following page.

Generalized catalysis. Traditional theory of catalysis has been successfully constructed on the concept of creating alternative reaction pathways of lower kinetic barriers. In this regime, the catalyst can only speed up a chemical reaction; it can never alter the spontaneous direction of the chemical reaction. However, according to recent result derived by the Lu group, there could be another general type of energy-flow-driven catalysts that can outperform traditional catalysts when it is exposed to a time-changing signal or environment. For example, certain catalytic reaction pathways could harness the energy from a time-varying environment and convert that energy to either (1) invert or (2) strengthen a spontaneous chemical reaction. When the reaction is inverted, the catalyst resembles a thermal engine that pumps the reaction backward, converting low free energy products back into high free energy reactants. When the reaction is strengthened, the catalyst assists the spontaneous reaction by utilizing the active dissipation of energy into the thermal bath, a notable distinction from the traditional catalysis mechanism. Moreover, Lu group researchers have derived a universal design principle to assist experiments to identify and design the optimal reaction pathways of these new type of catalysts.

Information sensors. Complex reaction networks are ubiquitous in chemical and biological systems. Such reaction networks not only allow atom exchange and energy transfer among molecules but also transfer information. Taking chemotaxis as an example, a single cell could couple the internal chemical reaction with the external concentration of food or toxins via a simple ligand-binding sensory network, thus enabling the environmental information to be transduced and computed by the internal chemical reaction network. The result would then be generation of environmentwise responses such as swimming to food or flee from danger. Inspired by the delicate yet robust information flow in the biochemical reaction networks of the living organisms, the Lu group researchers are working toward a general theory to guide the design of chemical reaction information processors. Recently, the group has shown that even a single receptor molecule can transduce multiple channels of information, allowing for chemical reaction networks to perform multiplexing information transduction that is commonly found in electronic information transducers.