Standard thermodynamics pertains to a system in equilib­rium. The meaning of equilibrium is that all fields such as temperature, pressure, magnetic, electric fields, etc., are held fixed, and the system is allowed sufficient time so that all dy­namical variables, e.g., position, momentum, and their func­tions, remain constant in time, on the average. If any of the aforesaid fields is changed to another value, the system, in general, is expected to come to a new equilibrium after a time much longer than what is known as the 'relaxation time'. Standard thermodynamics, however, does not touch upon the issue of the relaxation time or the time-evolution of the sys­tem. In recent years, there has been an upsurge of interest in nanoscience, especially in the context of biology and ma­terials, wherein the systems of interest are so tiny that they are hardly ever in equilibrium. Therefore, there is a need to go beyond standard thermodynamics and treat fluctuating, time-dependent effects. Stochastic Thermodynamics is one such important development that is pedagogically reviewed in this article. Our treatment will be restricted to classical systems.

Two-level quantum systems have their ubiquitous presence in chemistry and physics---in the basic ideas of bonding of atoms based on the superposition of two quantum states; in quantum optics and laser physics; in magnetic resonance; and a multitude of other phenomena. The underlying theory is well-described in many textbooks. This article aims to go beyond textbooks and familiarize university students (and hopefully excite them) about several related topics of great contemporary interest in chemistry and physics of materials, remaining however within their accessible realm. These topics are of current research activity, including tunneling centers in solids, coherent preservation of quantum information in qubits, hybridization of orbitals in carbon leading to materials such as graphene, the Berry phase, and its implication for magnetic monopoles, topological solids, and Rashba spin-split bands, etc. In discussing these themes, references are made to textbooks of quantum mechanics, but the connection is provided to advanced areas in a manner that is pedagogical and not forbidding to students.

We investigate here electron transport in a tight-binding chain under the action of a time-dependent force field. From the exact results for the mean-squared displacement, we discuss various special cases of zero field, static field, and oscillatory field. The consequent delocalization and localization phenomena make the tight-binding chain a textbook example for studying quantum coherent motion.