Onsager Reciprocal Relations

It is impossible to simultaneously know with perfect accuracy certain pairs of complementary physical properties of a particle. The most common example is the position \(x\) and momentum \(p\). The principle states that the product of their uncertainties, \(\Delta x\) and \(\Delta p\), must be greater than or equal to a specific value: \(\Delta x \Delta p \ge \frac{\hbar}{2}\).

A non-Newtonian fluid is one whose viscosity changes under an applied shear stress. Unlike a Newtonian fluid where viscosity is constant, its flow properties are not described by a linear relationship between shear stress (\(\tau\)) and shear rate (\(\dot{\gamma}\)). This dependency can manifest as shear-thinning (viscosity decreases with stress) or shear-thickening (viscosity increases with stress).

The oxidation state, or oxidation number, is a hypothetical charge that an atom would have if all its bonds to different atoms were 100% ionic. It provides a way to track electron transfer in redox reactions. An increase in oxidation state signifies oxidation, while a decrease signifies reduction. This formalism simplifies the analysis of complex chemical reactions.

Thermate is an incendiary composition that enhances standard thermite. It is typically a mixture of thermite, barium nitrate (\(Ba(NO_3)_2\)), and sulfur. The barium nitrate acts as an oxidizer, increasing the thermal output and making the reaction less dependent on atmospheric oxygen. Sulfur is added primarily to lower the ignition temperature, making the mixture easier and more reliably ignited.

Plasticity is the theory describing the deformation of a solid material undergoing non-reversible changes of shape in response to applied forces. Unlike elasticity, where deformation is recovered upon unloading, plastic deformation is permanent. The theory involves a yield criterion to define the onset of plasticity, a flow rule to describe the evolution of plastic strain, and a hardening rule.

Thixotropy and rheopexy describe time-dependent changes in viscosity. A thixotropic fluid's viscosity decreases over time under constant shear stress (e.g., yogurt becomes runnier when stirred). A rheopectic (or anti-thixotropic) fluid's viscosity increases over time under constant shear (e.g., some lubricants). These effects are reversible; the fluid returns to its original state after a period of rest.

A quantum mechanical phenomenon where a wavefunction can propagate through a potential energy barrier. Classically, a particle lacking sufficient energy to surmount a barrier would be reflected. However, due to the wave-like nature of particles, there is a non-zero probability that the particle can appear on the other side of the barrier, effectively 'tunneling' through it.

Electrochemical potential, \(\bar{\mu}_i\), quantifies the total energy of a charged species `i` in a system. It combines the chemical potential, \(\mu_i\), which accounts for concentration and intrinsic properties, with the electrostatic potential energy, \(z_i F \phi\). The formula is \(\bar{\mu}_i = \mu_i + z_i F \phi\), where \(z_i\) is the ion's charge, \(F\) is the Faraday constant, and \(phi\) is the local electric potential.

A solar cell's core is a p-n junction, an interface between p-type and n-type semiconductor materials. This junction creates a built-in electric field in a depletion region. When photons with sufficient energy strike the semiconductor, they create electron-hole pairs. The electric field separates these charge carriers, driving electrons to the n-side and holes to the p-side, generating a voltage.

The Weissenberg effect is a phenomenon in viscoelastic fluids where the fluid climbs up a rotating rod inserted into it. This is contrary to the behavior of Newtonian fluids, which are pushed outwards by centrifugal force, forming a vortex. The effect is caused by normal stress differences that develop in the fluid under shear.

A Pourbaix diagram, also known as a potential/pH diagram, is a thermodynamic chart that maps the stable equilibrium phases of an aqueous electrochemical system. It graphically shows the conditions of potential (\(E_H\)) and pH under which a metal is immune (thermodynamically stable), passivated (forms a stable protective film), or susceptible to corrosion (forms soluble ions).