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Projekt P3


Asymptotic Validity of the Jarzynski Relation for Non-Gibbsian Initial States in Isolated Quantum Systems


Jochen GemmerRobin SteinigewegKristel Michielsen


The last decades have witnessed a revived interest in tracing statistical mechanics back to pure state quantum mechanics. Recent (or not so recent) concepts like "typicality" or "eigenstate thermalization hypothesis" (ETH) essentially replace classical origins of (subjective) uncertainty like mixing or ergodicity by fundamental, dominant pure state quantum uncertainties in order to explain the occurrence of equilibrium, even though the quantum state of the full system is and always remains pure.

The entity of non-equilibrium thermodynamics, however, encompasses more general principles than the mere occurrence of equilibrium. Among those are the so-called fluctuation relations, the most prominent of them being possibly the Jarzynski relation (JR). The latter describes the probability distributions of work associated with processes driven arbitrarily far from equilibrium. Experimental evidence confirms that the JR is very widely valid. Derivations of the JR, classical or quantum, usually rely massively on the system in quest being initially strictly in a Gibbsian state. This starting point, however, is strongly at odds with the afore mentioned results in the field of thermalization of closed quantum systems: There, the principal notion of any ensemble is explicitly avoided and one aims at deriving everything from the dynamics of pure states.

With this project we want to arrive at the JR from the same point of departure: the concept of the full system state being possibly pure. We intend to analyze if the standard JR or other fluctuation relations hold for pure initial states living in very narrow energy shells. Since such a "pure state JR" cannot hold for all systems (counterexamples exist), this is an attempt to shift the JR from resting on specific properties of the initial state to resting on specific properties of the system. We suppose the key properties to be the accordance with some form of the ETH together with an exponentially growing density of states.