<P> Moreover, the slopes of the derivatives of ΔG and ΔH converge and are equal to zero at T = 0 . This ensures that ΔG and ΔH are nearly the same over a considerable range of temperatures and justifies the approximate empirical Principle of Thomsen and Berthelot, which states that the equilibrium state to which a system proceeds is the one that evolves the greatest amount of heat, i.e., an actual process is the most exothermic one . (Callen, pp. 186--187) </P> <P> One model that estimates the properties of an electron gas at absolute zero in metals is the Fermi gas . The electrons, being Fermions, must be in different quantum states, which leads the electrons to get very high typical velocities, even at absolute zero . The maximum energy that electrons can have at absolute zero is called the Fermi energy . The Fermi temperature is defined as this maximum energy divided by Boltzmann's constant, and is of the order of 80,000 K for typical electron densities found in metals . For temperatures significantly below the Fermi temperature, the electrons behave in almost the same way as at absolute zero . This explains the failure of the classical equipartition theorem for metals that eluded classical physicists in the late 19th century . </P> <P> A Bose--Einstein condensate (BEC) is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near absolute zero . Under such conditions, a large fraction of the bosons occupy the lowest quantum state of the external potential, at which point quantum effects become apparent on a macroscopic scale . </P> <P> This state of matter was first predicted by Satyendra Nath Bose and Albert Einstein in 1924--25 . Bose first sent a paper to Einstein on the quantum statistics of light quanta (now called photons). Einstein was impressed, translated the paper from English to German and submitted it for Bose to the Zeitschrift für Physik, which published it . Einstein then extended Bose's ideas to material particles (or matter) in two other papers . </P>

At what point is the temperature in °f almost exactly three times that in °c