Under what conditions do quantum systems thermalize

Lídia del Rio, Adrian Hutter, Renato Renner +1 more

Locally thermal quantum systems may contradict traditional thermodynamics: heat can flow from a cold body to a hotter one, if the two are highly entangled. We show that to recover thermodynamic laws, we must use a stronger notion of thermalization: a system S is thermal relative to a reference R if S is both locally thermal and uncorrelated with R. Considering a general quantum reference is particularly relevant for a thermodynamic treatment of nanoscale quantum systems. We derive a technical condition for relative thermalization in terms of conditional entropies. Established results on local thermalization, which implicitly assume a classical reference, follow as special cases.

Osamu Fukushima

Jesko Sirker, Nikolaos P. Konstantinidis, F. Andraschko +1 more

We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization process. We also show that this approach is useful to investigate thermalization based on a finite-size scaling of numerical data. The condition follows from an exact representation of the observable as the sum of a projection onto the local conserved charges of the system and a projection onto the nonlocal ones. We show that thermalization requires that the time average of the latter part vanishes in the thermodynamic limit while time and statistical averages for the first part are identical. As an example, we use this thermalization condition to analyze exact diagonalization data for a one-dimensional spin model. We find that local correlators do thermalize in the thermodynamic limit, although we find no indications that the eigenstate thermalization hypothesis applies.

Kurt A. Jacobs, Maxim Olshanii, Vanja Dunjko

Marco Cattaneo, Marco Baldovin, Dario Lucente +2 more

We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables—such as particle energies in physically relevant random quadratic Hamiltonians—is typical for large systems ( N ≫ 1 ) with initial conditions drawn from the microcanonical distribution. Moreover, we show that thermalization can also arise from nontypical initial conditions, where only a finite fraction of the normal modes is excited. A different choice of initial conditions, such as all the initial energy localized in a single particle, instead leads to energy equipartition without thermalization. Since the models we consider are integrable, our findings provide a general dynamical basis for an approach to thermalization that bypasses chaos and ergodicity, focusing instead on the physical requirement that thermodynamic observables depend on a large number of normal modes, and they build a bridge between the classical and quantum theories of thermalization.

Karamoko Soumahoro, Alison Valbuena, Roman Senkov