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We propose a duality between thermodynamics and computational complexity, elevating the difficulty of a computational task to the status of a thermodynamic variable. By introducing a complexity measure C as a novel coordinate, we formulate…
When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (covary).…
We are interested in the computational study of shock hydrodynamics, i.e. problems involving compressible solids, liquids, and gases that undergo large deformation. These problems are dynamic and nonlinear and can exhibit complex…
Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects…
Previous approaches of emergent thermalization for condensed matter based on typical wavefunctions are extended to generate an intrinsically quantum theory of gases. Gases are fundamentally quantum objects at all temperatures, by virtue of…
We present a systematic expansion in the ratio between the level spacing and temperature and employ it to evaluate differences between statistical mechanics and thermodynamics in finite disordered systems. These differences are related to…
Theory of Relativity (Special and General) is one of the most influential theories of the 20th century and has changed the way we view the world. It is part of many undergraduate curriculums and it is often suggested that it should be…
The specific heat and susceptibilities for the two- and one-dimensional spin--orbital models are calculated in the framework of a spherically symmetric self-consistent approach at different temperatures and relations between the parameters…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
The tasks of identifying separation structures and clusters in flow data are fundamental to flow visualization. Significant work has been devoted to these tasks in flow represented by vector fields, but there are unique challenges in…
Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…
Two dimensional quantum R$^2$-gravity is formulated in the semiclassical method. The thermodynamic properties,such as the equation of state, the temperature and the entropy, are explained. The topology constraint and the area constraint are…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
In this paper we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space valued data. These kind of data appear when dealing with nonlinear color spaces such as HSV, and they can be obtained by…
We show how the macroscopic state variables pressure, entropy and temperature of equilibrium thermodynamics can be consistently derived from the (quantum) chaotic spectral structure of one or two particles in two-dimensional domains. This…
A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose…
We propose a new formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second…
We present a state-of-the-art report on visualization in astrophysics. We survey representative papers from both astrophysics and visualization and provide a taxonomy of existing approaches based on data analysis tasks. The approaches are…
Thermodynamics is usually formulated on the presumption that the observer has complete information about the system he/she deals with: no parasitic current, exact evaluation of the forces that drive the system. For example, the acclaimed…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a given problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem…