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Universal Boltzmann Framework Arbitrarily Far From Equilibrium

We have successfully generalized Boltzmann's equilibrium statistical mechanics into a powerful framework that describes systems that are arbitrarily far from equilibrium and steady state. In 2022, we demonstrated that the language of equilibrium thermodynamics can be developed for any system with a well-defined state distribution (Phys. Rev. Lett. 2022). More recently, we have established a more powerful trajectory probability theory analogous to Boltzmann's distribution in equilibrium statistical physics, and it has become foundational for understanding complex non-equilibrium dynamics and especially how non-equilibrium systems respond to changes in their environments (Phys. Rev. E 2025 & arXiv 2025).

 

- Key Publications:​

• Z. Lu, H. Qian. "Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations" Phys. Rev. Lett. 128, (2022): 150603. 

• J. Zheng, Z. Lu, "Universal Response Inequalities Beyond Steady States via Trajectory Information Geometry", in press at Phys. Rev. E, (2025) (PDF available here.)

• J. Zheng, Z. Lu, "Spatial Correlation Unifies Nonequilibrium Response Theory for Arbitrary Markov Jump Processes", arXiv:2501.01050 (2025)​​

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Oscillation-Driven Catalysis

Since 2023, our group has predicted and explained how oscillating environments can drive chemical reactions into surprising behaviors, such as inverting thermodynamically spontaneous reactions. We developed a universal geometric non-equilibrium framework that provides both universal theorems and practical design rules for a new class of oscillation-driven catalysts that can harness energy from oscillating environments. One significant difference between the new type of catalysis and traditional textbook understanding of catalysis is that the new design of catalysis allows for (and even utilizes) high energy barriers, which is only expected under time-changing environments.

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- Key Publications:​​

• Z. Zhang, Z. Lu, ​"Non-equilibrium Theoretical Framework and Universal Design Principles of Oscillation-Driven Catalysis",  Journal of Physical Chemistry Letters, 14 (2023): 7541.    (Cover)

• Z. Zhang, V. Du, Z. Lu. "Energy landscape design principle for optimal energy harnessing by catalytic molecular machines." Physical Review E 107 (2023): L012102. 

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Biological Information Transduction

How does information transduce at the microscopic scale within biological cells? Our group established a stochastic information-theoretical framework for understanding biological information sensing beyond equilibrium or stationarity (J. Chem. Phys., 2024). By going beyond stationary statistics and studying dynamical trajectories, we have demonstrated that even a single sensor molecule could perform multiplex sensing -- simultaneously report multiple environmental variables (Phys. Rev. Research, 2023). Furthermore, we have established a universal non-equilibrium information benchmark for biological sensors (PRX Life, 2024)

 

We also demonstrated that molecules not only transduce information, but can also compute and process information! Very recently, we showed that even a single molecule can use its complex energy landscapes to effectively discern and respond to temporal patterns, realizing a single-molecule automaton (J. Chem. Phys., 2025).

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- Key Publications:​​
   

• A. Pagare*, Z. Zhang*, J. Zheng*, Z. Lu, "Stochastic Distinguishability of Markovian Trajectories", Journal of Chemical Physics, 160 (2024): 171101. 

• A. Pagare*, SH. Min*, Z. Lu. "Theoretical upper bound of multiplexing in biological sensory receptors"  Physical Review Research, 5 (2023): 023032.

• A. Pagare, Z. Lu, "Mpemba-Like Sensory Withdrawal Effect", Phys. Rev. X Life, 2 (2024): 043019. 

• Z. Zhang, Z. Lu, "Kinetic frustration enables single-molecule computation", J. Chem. Phys., 162 (2025): 134102. 

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Non-Equilibrium Shortcuts beyond the Mpemba Effect

Dr. Lu pioneered the study of the non-equilibrium Mpemba effect, where certain systems may cool faster by pre-heating. This foundational work initiated the field of non-equilibrium anomalous processes and has become highly cited, applied to a wide range of systems, ranging from classical colloids to quantum dynamics. More recently, Lu group has generalized this concept to encompass a wide variety of non-equilibrium chemical processes, such as self-assembly, far beyond thermal effects (J. Chem. Phys., 2023). To assist the speedy simulation of non-equilibrium controlled stochastic thermodynamic systems, we have also recently extended the kinetic Monte Carlo algorithm for time-dependent and feedback-controlled dynamics (J. Chem. Phys., 2024).

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- Key Publications:​

• Chittari, Supraja S., and Z. Lu. "Geometric approach to nonequilibrium hasty shortcuts", Journal of Chemical Physics, 159 (2023): 084106.   

• Chittari, Supraja S., and Z. Lu, "Revisiting Kinetic Monte Carlo Algorithms for Time-dependent Processes: from open-loop control to feedback control", J. Chem. Phys. 161 (2024): 044104.