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An ultracold analogue to star formation: Spontaneous concentration of energy in trapped quantum gases

Stars form when cold cosmic nebulae spontaneously develop hot spots that steadily intensify until they reach fusion temperatures. Without this process, the universe would be dark and dead. Yet the spontaneous concentration of heat is exactly what the Second Law of Thermodynamics is in most cases supposed to forbid. The formation of protostars has been much discussed, for its consistency with the Second Law depends on a thermodynamical property that is common in systems whose strongest force is their own gravity, but otherwise very rare: negative specific heat. Negative specific heat turns the world upside down, thermodynamically; it implies that entropy increases when energy flows from lower to higher energy subsystems, opposite to the usual direction. Recent experiments have reported negative specific heat in melting atomic clusters and fragmenting nuclei, but these arguably represent transient phenomena outside the proper scope of thermodynamics. Here we show that the counter-intuitive thermodynamics of spontaneous energy concentration can be studied experimentally with trapped quantum gases, by using optical lattice potentials to realize weakly coupled arrays of simple dynamical subsystems that share the peculiar property of self-gravitating protostars, of having negative micro-canonical specific heat. Numerical solution of real-time evolution equations confirms the spontaneous concentration of energy in such arrays, with initially dispersed energy condensing quickly into dense 'droplets'. We therefore propose laboratory studies of negative specific heat as an elusive but fundamentally important aspect of thermodynamics, which may shed fresh light on the general problem of how thermodynamics emerges from mechanics.