Related papers: Higher-dimensional nonlinear thermodynamic formali…

The accurate determination of transport coefficients in numerical simulations is becoming increasingly important in a wide range of applications. Here we consider the linear response in systems driven away from thermal equilibrium into a…

A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the…

We present in detail a Langevin formalism for constructing stochastic dynamical equations for active-matter systems coupled to a thermal bath. We apply the formalism to clarify issues of principle regarding the sources and signatures of…

In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…

A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a…

We derive a Thermodynamic Uncertainty Relation bounding the mean squared displacement of a Gaussian process with memory, driven out of equilibrium by unbalanced thermal baths and/or by external forces. Our bound is tighter with respect to…

An irreversible thermodynamical theory of solids is presented where the kinematic quantities are defined in an automatically objective way. Namely, auxiliary elements like reference frame, reference time and reference configuration are…

We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density,…

Some nonlinear extensions of the vector maximality statement established by Goepfert, Tammer and Zalinescu [Nonl. Anal., 39 (2000), 909-922] are given. Basic instruments for these are the Brezis-Browder ordering principle [Advances Math.,…

In this paper we derive Kl\"umper-Batchelor-Pearce-Destri-de Vega type nonlinear integral equations for describing the thermodynamics in the sine-Gordon model, when a chemical potential coupled to the topological charge is also present in…

We compare two approaches to the construction of the thermodynamics of a one-dimensional periodic system of spinless point bosons: the Yang--Yang approach and a new approach proposed by the author. In the latter, the elementary excitations…

The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs and how we treated it. It is demonstrated that the Guyer-Krumhansl equation…

On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…

We introduce a family of Hamiltonian models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases Fourier law is verified…

We study the model of a strongly non-linear chain of particles coupled to two heat baths at different temperatures. Our main result is the existence and uniqueness of a stationary state at all temperatures. This result extends those of…

Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature…

The forms of Euler and Gibbs-Duhem relations discussed in thermodynamics of extensive systems are shown to hold also for nonextensive systems with long-range interactions with a novel interpretation of entities appearing therein. In this…

This is an expository article, originally written in Japanese, on a dynamical system over a non-archimedean field. The main viewpoint is from complex and non-archimedean potential theories. After quickly introducing the Berkovich projective…

We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the…

Thermal models have proven to be an useful and simple tool used to make theoretical predictions and data analysis in relativistic and ultra-relativistic heavy ion collisions. A new version of these models is presented here, incorporating a…