Celebrating 360 years of Philosophical Transactions

Thévenin's theorem plays a pivotal role in electrical circuit analysis, offering a solution to the challenges posed by variable loads within a circuit. In practical applications, it is common to encounter circuits where certain elements remain fixed while others fluctuate, often referred to as the "load." A typical household electrical outlet serves as a prime example of a variable load, as it can be connected to a variety of appliances, each with its own unique electrical...

Parseval's theorem is a fundamental concept in signal processing and harmonic analysis. It asserts that for a periodic function, the average power of the signal over one period equals the sum of the squared magnitudes of all its complex Fourier coefficients. This theorem, named after Marc-Antoine Parseval, provides a powerful tool for analyzing the energy distribution in signals.
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which...

The second law of thermodynamics can be stated in several different ways, and all of them can be shown to imply the others. The Clausius’ statement of the second law of thermodynamics is based on the irreversibility of spontaneous heat flow. It states that heat will not flow from the colder body to the hotter body unless some other process is involved. Additionally, as per the Kelvin’s statement, it is impossible to convert the heat from a single source into work without any other...

Social traps are negative situations where people get caught in a direction or relationship that later proves to be unpleasant, with no easy way to back out of or avoid. The concept was orignally introduced by John Platt who applied psychology to Garrett Hardin's "Tragedy of the Commons", where in New England herd owners could let their cattle graze in the common ground. This situation seems like a good idea, but an individual could have an advantage. If they owned...