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Reaction–diffusion equations are commonly used to model a diverse array of complex systems, including biological, chemical, and physical processes. Typically, these models are phenomenological, requiring the fitting of parameters to experimental data. In the present work, we introduce a novel formalism to construct reaction–diffusion models that is grounded in the principle of maximum entropy. This new formalism aims to incorporate various types of experimental data, including ensemble currents, distributions at different points in time, or moments of such. To this end, we expand the framework of Schrödinger bridges and maximum caliber problems to nonlinear interacting systems. We illustrate the usefulness of the proposed approach by modeling the evolution of (i) a morphogen across the fin of a zebrafish and (ii) the population of two varieties of toads in Poland, so as to match the experimental data. 

Evanescent random walks are instances of stochastic processes that terminate at a specific rate. They have proved relevant in modeling diverse behaviors of complex systems from protein degra- dation in gene networks (Ali and Brewster (2022), Ghusinga, et al. (2017), and Ham, et al. (2024)) and “nonprocessive” motor proteins (Kolomeisky and Fisher (2007)) to decay of diffusive radioactive matter (Zoia (2008)). The present work aims to extend a well-established estimation and control problem, the so-called Schr¨odinger’s bridge problem, to evanescent diffusion processes. Specifically, the authors seek the most likely law on the path space that restores consistency with two marginal densities — One is the initial probability density of the flow, and the other is a density of killed particles. The Schr¨odinger’s bridge problem can be interpreted as an estimation problem but also as a control problem to steer the stochastic particles so as to match specified marginals. The focus of previous work in Eldesoukey, et al. (2024) has been to tackle Schr¨odinger’s problem involving a constraint on the spatio-temporal density of killed particles, which the authors revisit here. The authors then expand on two related problems that instead separately constrain the temporal and the spatial marginal densities of killed particles. The authors derive corresponding Schr¨odinger systems that contain coupled partial differential equa- tions that solve such problems. The authors also discuss Fortet-Sinkhorn-like algorithms that can be used to construct the sought bridges numerically. 

A class of signed joint probability measures for $n$arbitrary quantum observables is derived and studied based on quasicharacteristic functions with symmetrized operator orderings of Margenau-Hill type. It is shown that the Wigner distribution associated with these observables can be rigorously approximated by such measures. These measures are given by affine combinations of Dirac delta distributions supported over the finite spectral range of the quantum observables and give the correct probability marginals when coarse-grained along any principal axis. We specialize to bivariate quasiprobability distributions for the spin measurements of spin- $1/2$particles and derive their closed-form expressions. As a side result, we point out a connection between the convergence of these particle approximations and the Mehler-Heine theorem. Finally, we interpret the supports of these quasiprobability distributions in terms of repeated thought experiments. Published by the American Physical Society2025 

Physical systems transition between states with finite speed that is limited by energetic costs. In this work, we derive bounds on transition times for general Langevin systems that admit a decomposition into reversible and irreversible dynamics, in terms of the Wasserstein distance between states and the energetic costs associated with respective reversible and irreversible currents. For illustration we discuss Brownian particles subject to arbitrary forcing and an RLC circuit with time-varying inductor. 

We consider overdamped Brownian particles with two degrees of freedom (DoF) that are confined in a time- varying quadratic potential and are in simultaneous contact with heat baths of different temperatures along the respective DoF. The anisotropy in thermal fluctuations can be used to extract work by suitably manipulating the confining potential. The question of what the maximal amount of work that can be extracted is has been raised in recent work, and has been computed under the simplifying assumption that the entropy of the distribution of particles (thermodynamic states) remains constant throughout a thermodynamic cycle. Indeed, it was shown that the maximal amount of work that can be extracted amounts to solving an isoperimetric problem, where the 2-Wasserstein length traversed by thermodynamic states quantifies dissipation that can be traded off against an area integral that quantifies work drawn out of the thermal anisotropy. Here, we remove the simplifying assumption on constancy of entropy. We show that the work drawn can be computed similarly to the case where the entropy is kept constant while the dissipation can be reduced by suitably tilting the thermodynamic cycle in a thermodynamic space with one additional dimension. Optimal cycles can be locally approximated by solutions to an isoperimetric problem in a tilted lower-dimensional subspace. 

Abstract A typical model for a gyrating engine consists of an inertial wheel powered by an energy source that generates an angle-dependent torque. Examples of such engines include a pendulum with an externally applied torque, Stirling engines, and the Brownian gyrating engine. Variations in the torque are averaged out by the inertia of the system to produce limit cycle oscillations. While torque generating mechanisms are also ubiquitous in the biological world, where they typically feed on chemical gradients, inertia is not a property that one naturally associates with such processes. In the present work, seeking ways to dispense of the need for inertial effects, we study an inertia-less concept where the combined effect of coupled torque-producing components averages out variations in the ambient potential and helps overcome dissipative forces to allow sustained operation for vanishingly small inertia. We exemplify this inertia-less concept through analysis of two of the aforementioned engines, the Stirling engine, and the Brownian gyrating engine. An analogous principle may be sought in biomolecular processes as well as in modern-day technological engines, where for the latter, the coupled torque-producing components reduce vibrations that stem from the variability of the generated torque.