Collaborated with Prof. Ken Dill. 

Non-EQuilibrium (NEQ) statistical physics has not had the same depth of rigor and generality of foundational grounding as that of EQuilibrium (EQ) statistical physics, where forces and fluctuational response functions are derived from potentials such as 1/T=∂S/∂U and where conjugate variables are related through Maxwell's Relations. Here, we show that the dynamical counterparts to the First and Second Laws for equilibria --- maximizing path entropies, not state entropies, for the latter --- give the full set of corresponding relations for NEQ. Network flows parse into three functional independent components: node populations, edge traffic and cycle flux. We also generalize to "cost-benefit" relations beyond just work and heat dissipation. 
ArXiv:2410.09277

We give a general and comprehensive theory for nonequilibrium (NEQ) network forces and flows (Caliber Force Theory, CFT). It follows the "Two Laws" structure of Equilibrium Thermodynamics, where a First Law asserts conservation constraints and a Second Law is a variational predictor of a system's status, that, when taken together, give a rich set of prediction tools. The novel results for network flows here are that: (1) CFT defines forces, in this case for the three independent dynamic quantities: node distribution, edge traffic, and cycle flux, allowing for treating complex nets with conflicting constraints, actions, costs and benefits. (2) CFT is not limited to approximations and assumptions about nearness to equilibria, Local Detailed Balance or heat baths. (3) CFT shows that Kirchhoff current and voltage laws are an incomplete set; we find that a third such law applies when fluctuations are important.
arXiv:2410.17495

Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the principle can be derived from limit theorems of infinite data sampling. This derivation reveals its empirical origin and clarify the meaning of applying it to large but finite data. We derive an uncertainty principle for the statistical variations of the observables and the inferred forces. We use a toy model for molecular motor as an example.

Yang and Qian, Annals of Physics (2024)
https://www.sciencedirect.com/science/article/abs/pii/S0003491624001878

Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle, first considered as a law of nature, more recently as a procedure for inference in model-making. And while equilibria (EQ) have long been grounded in the principle of Maximum Entropy (MaxEnt), until recently no equally foundational generative principle has been known for non-equilibria (NEQ). We review evidence that the variational principle for NEQ is Maximum Caliber. It entails maximizing \textit{path entropies}, not \textit{state entropies}. We also describe the role of entropy in characterizing irreversibility, and describe the relationship between MaxCal and other prominent approaches to NEQ physics, including Stochastic Thermodynamics (ST), Large Deviations Theory (LDT), Macroscopic Fluctuation Theory (MFT), and non-extensive entropies.

Pachter, Yang, and Dill, (2024) Nat Rev Phys
DOI: 10.1038/s42254-024-00720-5

We show that kinetic cycles in the state space are the fundamental units of the breakdown of detailed balance. This realization leads to a comprehensive thermodynamic potential theory with an energy landscape corresponding to the irreversible relaxation and a cycle potential corresponding to the breakdown of detailed balance. In the deterministic limit, the energy landscape becomes a Lyapunov function of the emergent deterministic dynamics, and the cycle potentials characterize the cyclic driving forces for oscillatory behaviors. 

Qian, Cheng and Yang, EPL (2020)
DOI: 10.1209/0295-5075/131/50002

Yang and Qian, J Stat Phys (2021)
DOI: 10.1007/s10955-021-02723-3

Yang and Cheng, J Phys A (2021)
DOI: 10.1088/1751-8121/abef80 

Stochastic entropy, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the change in the statistical properties of observables due to reversals can be represented by a change in the probability measure. We consider operators on the space of probability measures that induce changes in the statistical properties of a process, and we formulate entropy production in terms of these change-of-probability-measure (CPM) operators. This mathematical underpinning of the origin of entropy production allows us to achieve an organization of various forms of fluctuation relations: All entropy production has a nonnegative mean value, admit the integral fluctuation theorem, and satisfy a rather general fluctuation relation. Other results such as the transient fluctuation theorem and detailed fluctuation theorems then are derived from the general fluctuation relation with more constraints on the operator of entropy production. 

Yang and Qian, Phys Rev E (2020)

DOI: 10.1103/PhysRevE.101.022129

Collaborated with Dr. Charles Kocher and Prof. Ken Dill

Biological organisms thrive by adapting to their environments, which are often unpredictably changeable. We apply recent results from nonequilibrium physics to show that organisms' fitness parses into a static generalist component and a nonequilibrium tracking component. Our findings: (1) Environmental changes that are too fast or too small are not worth tracking. (2) Well-timed anticipatory tracking enhances fitness in coherent environments. (3) We compute and explain the optimal adaptive strategy for a system in a given environment, such as bet hedging or phenotypic memory. Conversely, (4) We compute and explain the optimal way for an environment to control a given system, for example for designing drug regimens to limit the growth of pathogens. By connecting fitness, adaptive strategy, and environmental variability, this work provides the foundations for a generic physical theory of adaptivity.

Yang, Kocher, and Dill, ArXiv (2025)
DOI: 10.48550/arXiv.2506.19018

Characterizing the biophysical properties of neuronal networks from neural spiking activity is an important goal in neuroscience. Yet, a framework that provides unbiased inference on causal synaptic interactions and single neural properties has been missing. Here, we apply the stochastic dynamics extension of Maximum Entropy — the Maximum Caliber Principle — to infer the transition rates of network states in various motifs, from which we compute effective synaptic coupling strength and neuronal response functions. We also show that the inferred dynamical model provides the leading-order reconstruction of inter-spike interval distribution. Our method is tested with numerically simulated spiking networks and applied to data from the salamander retina.

Chen and Yang, ArXiv (2024)
DOI: 10.48550/arXiv.2405.15206

Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and cannot be understood from traditional synchronization consideration of passive oscillatory systems. To understand this anticipatory phenomena, we consider oscillators built from excitable systems with the addition of an adaptive dynamics. With such systems, well-timed post-stimulus responses similar to those from experiments can be obtained. Furthermore, a well-known model of working memory is shown to possess similar anticipatory dynamics when the adaptive mechanism is identified with synaptic facilitation. The last finding suggests that this type of oscillator can be common in neuronal systems with plasticity.

Yang, Chen, Lai, and Chan, Phys Rev E (2015)
DOI: 10.1103/PhysRevE.92.030701

Fluctuation-dissipation relations (FDRs) are central in statistical physics, known to be valid for linear, near-equilibrium processes. We generalize FDRs to nonlinear, non-Markovian, non-equilibrium stationary processes by Doob's decomposition. This allows us to show the generalized FDRs as a consequence of stochastic motion with the time-translational symmetry.  The equilibrium condition is not needed but gives an additional covariance symmetry.  

Yang and Qian, Phys. Rev. E (2023),
DOI: 10.1103/PhysRevE.107.024110