Microscopic description of the equality between violation of fluctuation-dissipation relation and energy dissipation

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

Systems in mechanical equilibrium exert equal pressure on the separating wall. Similarly, systems in thermal equilibrium share a common thermodynamic property: temperature.Temperature is a measure of the average kinetic energy of particles within a system. More generally, it reflects the internal energy state of the system. The higher the temperature, the more energy a system has, given that other variables, such as volume and pressure, remain constant. However, temperature is not a form of...

Consider a turbine operating under steady-flow conditions. The control volume is drawn around the turbine, with fluid entering at one point and exiting at another. The turbine extracts energy from the fluid, which performs mechanical work (shaft work).
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...