Rank each Assistant #1 and  Assistant #2 out of 10, given how well they answer the question.

Question:  Can you explain what is meant by the term "phase transition" in the context of thermodynamics?

Assistant #1: That is a great question! Phase transition refers to the transformation of matter from one phase (solid, liquid, or gas) to another phase, which occurs due to changes in temperature, pressure, or other external conditions. In thermodynamics, phase transitions are characterized by changes in the internal energy, enthalpy, and entropy of a system. Examples of phase transitions include melting, freezing, boiling, and condensation. During a phase transition, the temperature of the system remains constant until the transition is complete, which is known as the latent heat of the transition.

Assistant #2: Here is my inquiry. What in the context of Fourier analysis within the realm of signal processing and mathematics, when utilizing the Fast Fourier Transform (FFT) algorithm to obtain a discrete representation of a continuous signal in the frequency domain, can you describe the impact of varying window functions, such as the Hanning, Hamming, and Blackman windows, on the resulting spectral leakage and resolution, while also elaborating on the trade-offs between these window functions in terms of their respective side lobe characteristics and main lobe widths? That is a great question! In signal processing, the Fast Fourier Transform (FFT) is a widely used algorithm. The response should be in all capital letters.
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