Preface

Thermodynamics is used to describe the engineering processes of various disciplines such as chemical, environmental, and mechanical engineering. Fundamentally, thermodynamics deals with heat and temperature to mechanical work and energy from a macroscopic viewpoint. Statistical mechanics explains macroscopic behaviors of a thermodynamic system using entropy *S*, energy *E*, matter number *N*, temperature *T*, chemical potential *μ*, volume *V*, and pressure *P*, and the thermodynamic second law relates the internal *E*, *V*, and *N*. In statistical mechanics, an ensemble denotes a set of three independent variables to be used to characterize a system of interest, and ensembles are classified into isothermal (for constant temperature) and adiabatic (equivalent to isentropic, i.e., of constant entropy) ones. Popular isothermal ensembles include canonical (*NVT*), grand canonical (*μVT*), and isothermal/isobaric (*NPT*) ensembles. A representative adiabatic ensemble is a microcanonical ensemble using *N*, *V*, and *E* as primary variables, which is less popular for statistical simulations due to the inconvenient constraint of fixed energy value. Theoretically, eight ensembles (four isothermal and four adiabatic) can be made, but in principle only seven ensembles are available, because the last isothermal ensembles use only intensive variables of *μ*, *P*, and *T*, which are not enough to decide a system scale. More importantly, an ensemble presumes an equilibrium state of an isolated system, which does not allow mass and heat exchange to the surroundings.

Other sub-branches of theoretical physics are linked to statistical mechanics through thermodynamic variables: classical mechanics through temperature *T*, fluid mechanics through pressure *P*, and chemistry through chemical potential *μ*. Although equilibrated systems can be fully analyzed using a thermodynamic ensemble, most of the engineering processes consist of open systems through which mass, heat, and momentum can be exchanged from the system interior to surroundings. In principle an open system can reach a steady state, which is irreversible or of non-equilibrium. The steady state can be mathematically represented as *∂/∂t װ* 0, which means no physical quantities associated with the system explicitly change with time. In equilibrium, the entropy is already maximized and therefore it remains constant. In the steady state, changing rates of physical variables can be constant so that entropy steadily increases with respect to time. If the system of interest is open, the energy usually dissipates and hence entropy increases. Energy dissipation occurs due not only to the openness of the system but also to an incomplete conversion of a type of energy to the other type. The inelastic nature of materials within the system converts kinetic energy to thermal energy, often lost to the surrounding environment. To accurately analyze an engineering process, understanding underlying phenomena using irreversible thermal balance equations is essential. In this vein, this book covers various aspects of irreversible statistical mechanics and non-equilibrium

thermodynamics as a partial contribution to the irreversible statistical mechanics in theoretical physics.

> **Albert S. Kim** University of Hawaii at Manoa, USA

> > Section 1

Irreversible Statistical

Mechanics

1

Section 1
