Related papers: Tropical Limit for Configurational Geometry in Dis…

For classical discrete systems under constant composition, we re-examine how linear-nonlinear boundary in canonical ensemble, connecting a set of potential energy surface and that of microscopic configuration in thermodynamic equilibrium,…

For classical discrete systems under constant composition, a set of microscopic state dominantly contributing to thermodynamically equilibrium structure should depend on temperature and energy through Boltzmann factor, exp(-bE). Despite…

For classical discrete system under constant composition typically referred to substitutional alloys, we examine local nonlinearity in canonical average phi . We have respectively investigated the local and global behavior of nonlinearity…

For classical discrete systems under constant composition, statistical mechanics tells us that a set of microscopic state dominantly contributing to thermodynamically equilibrium state should depend on temperature as well as on many-body…

When we consider classical discrete systems under constant composition, their stable configuration in thermodynamic equilibrium can be typically obtained through the well-known canonica average phi. In configurational thermodynamics, phi as…

For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…

For substitutional crystalline solids typically referred to classical discrete system under constant composition, macroscopic structure in thermodynamically equilibrium state can be typically obtained through canonical average, where a set…

For classical discrete system under constant composition, typically reffered to as substitutional alloys, canonical average acts as nonlinear map F from a set of potential energy surface U to that of microscopic configuration in…

For classical discrete system under constant composition, we theoretically examine origin of nonlinearity in thermodynamic (so-called canonical) average w.r.t. many-body interactions, in terms of geometrical information in configuratin…

For classical systems, expectation value of macroscopic property in equilibrium state can be typically provided through thermodynamic (so-called canonical) average, where summation is taken over possible states in phase space (or in…

When spatial constraint for the constituents (e.g., atom or particle) of system is once given, disordered structure for non-interacting system in equilibrium states is symmetric with respect to equiatomic composition. Meanwhile, when the…

We explore how the thermodynamic properties and dynamics of a self-interstitial prismatic dislocation loop are affected by microscopic-scale variations in its geometric configuration, an aspect that rarely received attention in literature.…

Based on classical statistical thermodynamics, we develop a theoretical approach that provides new insight into how macroscopic and microscopic physical properties are bridged via crystal lattice for condensed mat- ters. We find that in…

For classical discrete systems under constant composition (specifically substitutional alloys), canonical average acts as a map from a set of many-body interatomic interactions to a set of configuration in thermodynamic equilibrium, which…

Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents…

In classical systems, we reexamine how macroscopic structures in equilibrium state connect with spatial con- straint on the systems: e.g., volume and density as the constraint for liquids in rigid box, and crystal lattice as the constraint…

For classical system under constant composition, macroscopic structure in thermodynamically equilibrium state can be determined through the so-called canonical average, including sum over possible microscopic states on phase space. Although…

For substitutional alloys, typically refered to as classical discrete systems under constant composition, we theoretically examine the role of hidden structure information on evolution of nonlinearity (i.e., correspondence between a set of…

Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of…

Thermal contact is the archetype of non-equilibrium processes driven by constant non-equilibrium constraints when the latter are enforced by reservoirs exchanging conserved microscopic quantities. At a mesoscopic scale only the energies of…