Related papers: Thermodynamics and the moment map
In this note, we analyze the relationships that should govern the use of thermodynamics in fluid mechanics in a way that we believe is understandable to mathematicians. We also aim to better define the reasons why mechanics and…
We introduce the notion of an extended moment in time, the duron. This is a region of temporal ambiguity which arises naturally in the nature of process which we take to be basic. We introduce an algebra of process and show how it is…
We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…
For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is equivariant and smooth. For the space of…
The thermodynamic interpretation of the Stephani Universes is studied in detail. The general expression of the speed of sound and of the thermodynamic schemes associated with a thermodynamic solution is obtained. The constraints imposed on…
We prove a convexity theorem for the image of the moment map of a Hamiltonian torus action on a $b^m$-symplectic manifold.
Phase transitions are ubiquitous across life, yet hard to quantify and describe accurately. In this work, we develop an approach for characterizing generic attributes of phase transitions from very limited observations made deep within…
Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to…
A thermodynamically consistent mathematical model for hydrogen adsorption in metal hydrides is proposed. Beside hydrogen diffusion, the model accounts for phase transformation accompanied by hysteresis, swelling, temperature and heat…
Completely positive trace preserving maps are essential for the formulation of the second law of thermodynamics. The dynamics of quantum systems, correlated with their environments, are in general not described by such maps. We explore how…
We provide a hydrodynamical description of a holographic theory with broken translation invariance. We use the fluid/gravity correspondence to systematically obtain both the constitutive relations for the currents and the Ward identity for…
Uniformity of the probability measure of phase space is considered in the framework of classical equilibrium thermodynamics. For the canonical and the grand canonical ensembles, relations are given between the phase space uniformities and…
We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a…
The ferrofluid dynamics theory is applied to thermodiffusive problems in magnetic fluids in the presence of magnetic fields. The analytical form for the magnetic part of the chemical potential and the most general expression of the mass…
We study a new spacetime which is shown to be the general geometrical background for Thermal Field Theories at equilibrium. The different formalisms of Thermal Field Theory are unified in a simple way in this spacetime. The set of…
Relativistic thermodynamics is constructed from the point of view of special relativistic hydrodynamics. A relativistic four-current for heat and a general treatment of thermal equilibrium between moving bodies is presented. The different…
Conversations about weather, environment, health, cuisine, and even politics, all involve the word "temperature". It was an attempt to understand the working of heat engines that gave the temperature a clear definition. In this Note we put…
In this paper we study in detail, both analytically and numerically, the dynamical properties of the triangle map, a piecewise parabolic automorphism of the two-dimensional torus, for different values of the two independent parameters…
Preparing general relativity for quantization in the Hamiltonian approach leads to the `problem of time,' rendering the world fundamentally timeless. One proposed solution is the `thermal time hypothesis,' which defines time in terms of…
We describe a classical thermodynamic model that reproduces the main features of the solid hydrogen phase diagram. In particular, we show how the general structure types that are found by electronic structure calculations and the quantum…