Related papers: Thermodynamic Semirings
We study the constructible Witt theory of \'etale sheaves of $\Lambda$-modules on a scheme $X$ for coefficient rings $\Lambda$ having finite characteristic not equal to 2 and prime to the residue characteristics of the scheme $X$. Our…
Three-dimensional icosahedral random tilings are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice points in orthogonal space. The specific heat shows a pronounced Schottky…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
We discuss a simple toy model which allows, in a natural way, for deriving central facts from thermodynamics such as its fundamental laws, including Carnot's version of the second principle. Our viewpoint represents thermodynamic systems as…
In this paper we remark that Shannon entropy can be expressed as a function of the self-information (i.e. the logarithm) and the inverse of the Lambert $W$ function. It means that we consider that Shannon entropy has the trace form: $-k…
Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show…
Thermodynamic properties such as temperature, pressure, and internal energy have been defined for finite binary strings from equilibrium distribution of a chosen computable measure. It is demonstrated a binary string can be associated with…
We give, for every finite group G, a combinatorial description of the ring of G-Witt vectors on a polynomial algebra over the integers. Using this description we show that the functor, which takes a ring with trivial action of G to its ring…
We show that there exists a natural way to define a condition of generalized thermal equilibrium between systems governed by Tsallis thermostatistics, under the hypotheses that i) the coupling between the systems is weak, ii) the structure…
Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In…
Three-dimensional icosahedral random tilings with rhombohedral cells are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice points in the orthogonal space. The internal…
The Witt ring of a complex flag variety describes the interesting -- i.e. torsion -- part of its topological KO-theory. We show that for a large class of flag varieties, these Witt rings are exterior algebras, and that the degrees of the…
Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp.…
We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to…
In this article we consider two spin$-1/2$ chains described, respectively, by the thermodynamic limit of the $XY$ model with the usual two site interaction, and an extension of this model (without taking the thermodynamics limit), called…
Small spin systems at the interface between analytical studies and experimental application have been intensively studied in recent decades. The spin ring consisting of four spins with uniform antiferromagnetic Heisenberg interaction is an…
Based on our previous work on an arithmetic analogue of Christol's theorem, this paper studies in more detail the structure of the lambda-ring $E_K = K \otimes W_{O_K}^a (O_{\bar{K}})$ of algebraic Witt vectors for number fields $K$. First…
The tight binding model is a minimalistic electronic structure model for predicting properties of materials and molecules. For insulators at zero Fermi-temperature we show that the potential energy surface of this model can be decomposed…
Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We…
In this paper, we derive both the Adam-Gibbs and the Rosenfield relations from the microscopic point of view and compare them with the numerical calculation for one and two dimensional systems. The comparison shows there is an excellent…