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1. A statistical mechanics framework for constructing nonequilibrium thermodynamic models

   https://doi.org/10.1093/pnasnexus/pgad417  

   Leadbetter, Travis ; Purohit, Prashant K ; Reina, Celia ( December 2023 , PNAS Nexus)

   Sharma, Pradeep (Ed.)

   Far-from-equilibrium phenomena are critical to all natural and engineered systems, and essential to biological processes responsible for life. For over a century and a half, since Carnot, Clausius, Maxwell, Boltzmann, and Gibbs, among many others, laid the foundation for our understanding of equilibrium processes, scientists and engineers have dreamed of an analogous treatment of nonequilibrium systems. But despite tremendous efforts, a universal theory of nonequilibrium behavior akin to equilibrium statistical mechanics and thermodynamics has evaded description. Several methodologies have proved their ability to accurately describe complex nonequilibrium systems at the macroscopic scale, but their accuracy and predictive capacity is predicated on either phenomenological kinetic equations fit to microscopic data or on running concurrent simulations at the particle level. Instead, we provide a novel framework for deriving stand-alone macroscopic thermodynamic models directly from microscopic physics without fitting in overdamped Langevin systems. The only necessary ingredient is a functional form for a parameterized, approximate density of states, in analogy to the assumption of a uniform density of states in the equilibrium microcanonical ensemble. We highlight this framework’s effectiveness by deriving analytical approximations for evolving mechanical and thermodynamic quantities in a model of coiled-coil proteins and double-stranded DNA, thus producing, to the authors’ knowledge, the first derivation of the governing equations for a phase propagating system under general loading conditions without appeal to phenomenology. The generality of our treatment allows for application to any system described by Langevin dynamics with arbitrary interaction energies and external driving, including colloidal macromolecules, hydrogels, and biopolymers. 

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2. Non-equilibrium early-warning signals for critical transitions in ecological systems

   https://doi.org/10.1073/pnas.2218663120  

   Xu, Li ; Patterson, Denis ; Levin, Simon Asher ; Wang, Jin ( January 2023 , Proceedings of the National Academy of Sciences)

   Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to avert a regime shift. We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions. We quantify the average flux as the nonequilibrium driving force and the dynamical origin of the nonequilibrium transition while the entropy production rate as the nonequilibrium thermodynamic cost and thermodynamic origin of the nonequilibrium transition. Average flux, entropy production, nonequilibrium free energy, and time irreversibility quantified by the difference in cross-correlation functions forward and backward in time can serve as early warning signals for critical transitions much earlier than other conventional predictors. We utilize a classical shallow lake model as an exemplar for our early warning prediction. Our proposed method is general and can be readily applied to assess the resilience of many other ecological systems. The early warning signals proposed here can potentially predict critical transitions earlier than established methods and perhaps even sufficiently early to avert catastrophic shifts. 

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3. Debates: Does Information Theory Provide a New Paradigm for Earth Science? Emerging Concepts and Pathways of Information Physics

   https://doi.org/10.1029/2019WR025270  

   Perdigão, Rui A. P. ; Ehret, Uwe ; Knuth, Kevin H. ; Wang, Jingfeng ( February 2020 , Water Resources Research)

   Entropy and Information are key concepts not only in Information Theory but also in Physics: historically in the fields of Thermodynamics, Statistical and Analytical Mechanics, and, more recently, in the field of Information Physics. In this paper we argue that Information Physics reconciles and generalizes statistical, geometric, and mechanistic views on information. We start by demonstrating how the use and interpretation of Entropy and Information coincide in Information Theory, Statistical Thermodynamics, and Analytical Mechanics, and how this can be taken advantage of when addressing Earth Science problems in general and hydrological problems in particular. In the second part we discuss how Information Physics provides ways to quantify Information and Entropy from fundamental physical principles. This extends their use to cases where the preconditions to calculate Entropy in the classical manner as an aggregate statistical measure are not met. Indeed, these preconditions are rarely met in the Earth Sciences due either to limited observations or the far‐from‐equilibrium nature of evolving systems. Information Physics therefore offers new opportunities for improving the treatment of Earth Science problems.

    

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4. Quantum entropy and central limit theorem

   https://doi.org/10.1073/pnas.2304589120  

   Bu, Kaifeng ; Gu, Weichen ; Jaffe, Arthur ( June 2023 , Proceedings of the National Academy of Sciences)

   We introduce a framework to study discrete-variable (DV) quantum systems based on qudits. It relies on notions of a mean state (MS), a minimal stabilizer-projection state (MSPS), and a new convolution. Some interesting consequences are: The MS is the closest MSPS to a given state with respect to the relative entropy; the MS is extremal with respect to the von Neumann entropy, demonstrating a “maximal entropy principle in DV systems.” We obtain a series of inequalities for quantum entropies and for Fisher information based on convolution, giving a “second law of thermodynamics for quantum convolutions.” We show that the convolution of two stabilizer states is a stabilizer state. We establish a central limit theorem, based on iterating the convolution of a zero-mean quantum state, and show this converges to its MS. The rate of convergence is characterized by the “magic gap,” which we define in terms of the support of the characteristic function of the state. We elaborate on two examples: the DV beam splitter and the DV amplifier.

    

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5. Exchange fluctuation theorems for strongly interacting quantum pumps

   https://doi.org/10.1116/5.0152186  

   Sone, Akira ; Soares-Pinto, Diogo O. ; Deffner, Sebastian ( September 2023 , AVS Quantum Science)

   We derive a general quantum exchange fluctuation theorem for multipartite systems with arbitrary coupling strengths by taking into account the informational contribution of the back-action of the quantum measurements, which contributes to the increase in the von-Neumann entropy of the quantum system. The resulting second law of thermodynamics is tighter than the conventional Clausius inequality. The derived bound is the quantum mutual information of the conditional thermal state, which is a thermal state conditioned on the initial energy measurement. These results elucidate the role of quantum correlations in the heat exchange between multiple subsystems.

    

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