Related papers: Thermodynamics and the moment map
We introduce a higher-order version of the tangent map of a morphism and find a matrix representation. We then apply this matrix to solve a conjecture by T. Yasuda regarding the semigroup of the higher Nash blowup of formal curves. We first…
We translate the equivariant decomposition theorem (in the case of a proper morphism of toric varieties) in to the language of combinatorially defined ``shifted minimal complexes''.
The main purpose of this paper is to give a simple and non-combinatorial proof of the toric Mori theory. Here, the toric Mori theory means the (log) Minimal Model Program (MMP, for short) for toric varieties. We minimize the arguments on…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
We analyze the canonical structure of a continuum model of ferromagnets and clarify known difficulties in defining a momentum density. The moments of the momentum density corresponding to volume-preserving coordinate transformations can be…
This paper surveys the role of moment maps in K\"ahler geometry. The first section discusses the Ricci form as a moment map and then moves on to moment map interpretations of the K\"ahler--Einstein condition and the scalar curvature…
Probabilistic approach to the description of translational motion of macrobodies indicates the emergence of additional order effects oriented in the direction of motion of the body
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
Thermodynamics is based on a coarse-grained approach, from which its fundamental variables emerge, effectively erasing the complicate details of the microscopic dynamics within a macroscopic system. The strength of Thermodynamics lies in…
The concept of temperature is one of the key ideas in describing the thermodynamical properties of a physical system. In classical statistical mechanics of ideal gases, the notion of temperature can be described in two different ways, the…
We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…
We derive a general formulation of the laws of irreversible thermodynamics in the presence of electromagnetism and gravity. For the handling of macroscopic material media, we use as a guide the field equations and the Noether identities of…
The detailed analysis of model of the hydrodynamical vortice on a plane is executed. The derivation of the corresponding equation and its simplified variant is given, a partial solutions are constructed. The question on application of…
Phenomenological thermodynamic theory describing the properties of metastable states in disordered ferromagnets and ferroelectrics with frustrative random interactions is developed and its ability to describe various nonergodic phenomena in…
The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…
The thermodynamical formalism is studied for renormalisable maps of the interval and the natural potential $-t \log|Df|$. Multiple and indeed infinitely many phase transitions at positive $t$ can occur for some quadratic maps. All unimodal…
The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant…
A short introduction on quantum thermodynamics is given and three new topics are discussed: 1) Maximal work extraction from a finite quantum system. The thermodynamic prediction fails and a new, general result is derived, the ``ergotropy''.…
The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. These lecture notes provide an…