We propose a new equilibrium concept: asymptotic ε-Nash equilibrium for 2 order two-player nonzero-sum games where each player has a control-free cost functional quadratic in the system states over an infinite horizon and each player’s control strategy is constrained to be continuous linear state feedback. Based on each player’s singular control problem, the asymptotic ε-Nash equilibrium implem...

In the algebraic formulation the thermodynamic pressure, or free energy, of a spin system is a convex continuous function P defined on a Banach space ~3 of translationally invariant interactions. We prove that each tangent functional to the graph of P defines a set of translationally invariant thermodynamic expectation values, l~Iore precisely each tangent functional defines a translationally i...

The seminal work of Huggett [“The risk-free rate in heterogeneous-agent incomplete-insurance economies”, Journal of Economic Dynamics and Control, 1993, 17(5-6), 953-969] showed that in a stationary recursive equilibrium, there exists a unique stationary distribution of agent types. However, the question remains open if an equilibrium’s individual state space might turn out to be such that eith...

We consider the computation of the coexistence pressure of the liquid-solid transition of a system of hard spheres from direct simulation of the inhomogeneous system formed from liquid and solid phases separated by an interface. Monte Carlo simulations of the interfacial system are performed in three different ensembles. In a first approach, a series of simulations is carried out in the isother...

This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the 'maximum entropy production' (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function (st) for non-equilibrium systems, analogous to the free energy concept of equilibrium thermodynamics. Spontaneous reduction...

This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the “maximum entropy production” (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function φst for non-equilibrium systems, analogous to the free energy concept of equilibrium thermodynamics. Spontaneous reductions...

The SEIR (Susceptible-Exposed-Infected-Recovered) model is used to describe the transmission of dengue virus. The main contribution is determining the role of the rainfall in Thailand in the model. The transmission of dengue disease is assumed to depend on the nature of the rainfall in Thailand. We analyze the dynamic transmission of dengue disease. The stability of the solution of the model is...

We illustrate how the Jarzynski equality (JE), which is the progenitor of non-equilibrium methods aimed at constructing free energy landscapes for molecular-sized fluctuating systems subjected to steered transformations, can be applied to derive equations of state for bulk systems. The key-step consists of physically framing the computational strategy of "total energy morphing", recently presen...

The most Malaria cases are occur along Thai-Mynmar border. Mathematical model for the transmission of Plasmodium falciparum and Plasmodium vivax malaria in a mixed population of Thais and migrant Burmese living along the Thai-Myanmar Border is studied. The population is separated into two groups, Thai and Burmese. Each population is divided into susceptible, infected, dormant and recovered subc...

We will study a mathematical model on the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics in the context of disease spread in vivo. The deterministic model requires us to analyze asymptotic stability of two distinct steady states, disease-free and endemic equilibria. Previous results have focused on investigating ...