Related papers: Configurational space discretization and free ener…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
We report a numerical calculation of the total number of disordered jammed configurations $\Omega$ of $N$ repulsive, three-dimensional spheres in a fixed volume $V$. To make these calculations tractable, we increase the computational…
A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths --- the rare trajectories that transit between the folded and unfolded ensembles --- using only thermodynamic information, such as a…
A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the Information-Processing Second Law (IPSL): the physical entropy of the universe can decrease if compensated by…
Regularization of control policies using entropy can be instrumental in adjusting predictability of real-world systems. Applications benefiting from such approaches range from, e.g., cybersecurity, which aims at maximal unpredictability, to…
We introduce an exactly solvable lattice model that reveals a universal finite-size scaling law for configurational entropy driven purely by geometry. Using exact enumeration via Burnside's lemma, we compute the entropy for diverse 1D, 2D,…
From thermodynamic origins, the concept of entropy has expanded to a range of statistical measures of uncertainty, which may still be thermodynamically significant. However, laboratory measurements of entropy continue to rely on direct…
Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…
Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…
Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a…
Isotropic pairwise interactions that promote the self assembly of complex particle morphologies have been discovered by inverse design strategies derived from the molecular coarse-graining literature. While such approaches provide an avenue…
The Jarzynski identity can be applied to instances when a microscopic system is pulled repeatedly but quickly along some coordinate, allowing the calculation of an equilibrium free energy profile along the pulling coordinate from a set of…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
When studying high-dimensional dynamical systems such as macromolecules, quantum systems and polymers, a prime concern is the identification of the most probable states and their stationary probabilities or free energies. Often, these…
We construct a configurational entropy measure in functional space. We apply it to several nonlinear scalar field models featuring solutions with spatially-localized energy, including solitons and bounces in one spatial dimension, and…
Molecular Density Functional Theory (MDFT) offers an efficient implicit- solvent method to estimate molecule solvation free-energies whereas conserving a fully molecular representation of the solvent. Even within a second order ap-…
The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is…
This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under…