question of thermalization to the union of the
bath and the system (6). Although ergodicity
and time-averaging can provide a justification
for entropy maximization in closed classical
mechanical systems, ergodicity is not applicable on the same scale at which statistical mechanics is successful, and time-averaging can
require exponentially long times (13, 41, 42).
The latter also obscures the fact that there is
in reality only one system, which, nevertheless,
is well modeled by an entropic ensemble (41).
Our study, as well as recent theoretical work
(11, 12, 35), hint at a microscopic origin for
entropy maximization in a single quantum state,
namely, that which is induced by the entanglement that we have measured. Quantum mechanics does not require time-averaging; a single
quantum state yields thermalized local observables, and these observables cannot distinguish
this thermalized pure state from a mixed thermal
ensemble of the same thermodynamic character.
Our measurements open up several avenues
for further investigation. Instead of operating
with a fixed total system size, it is possible to
study how thermalization and fluctuations depend on the size of the system considered (40).
Conversely, studying integrable Hamiltonians
where thermalization fails (43), as well as the
structure of the associated eigenstate spectrum
of such systems, could allow direct tests of the
relationship between conserved quantities and
thermalization of a quantum state. Lastly, the
application of these tools for characterizing the
presence of thermalization and entanglement
entropy could be powerful in studies of many-body localization, where one of the key experimental signatures is the logarithmic growth of
entanglement entropy at long times and the suppression of precisely the thermalization that we
have measured in this work (20, 44–47).
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We acknowledge helpful discussions with S. Choi, S. Dickerson,
J. Eisert, M. Foss-Feig, D. Greif, M. Headrick, D. Huse, M. Olshanii,
C. Regal, J. Schachenmayer, and M. Wall. We are supported by
grants from the NSF, including an NSF Graduate Research
Fellowship (to M.R.); the Gordon and Betty Moore Foundation’s
Emergent Phenomena in Quantum Systems initiative (grant
GBMF3795); and the Multidisciplinary University Research Initiative
programs of the Air Force Office of Scientific Research and the
Army Research Office.
Materials and Methods
Figs. S1 to S3
Tables S1 and S2
11 March 2016; accepted 11 July 2016
Northward migration of the eastern
Himalayan syntaxis revealed
by OSL thermochronometry
Georgina E. King,1,2 Frédéric Herman,1 Benny Guralnik3
Erosion influences the dynamical evolution of mountains. However, evidence for the impact of
surface processes on tectonics mostly relies on the circumstantial coincidence of rugged
topography, high stream power, erosion, and rock uplift. Using the optically stimulated
luminescence (OSL) thermochronometry technique, we quantified the spatial and temporal
exhumation of the eastern Himalayan syntaxis. We found increasing exhumation rates within the
past million years at the northeast end of the Namche Barwa–Gyala Peri dome. These observations
imply headward propagation of erosion in the Parlung River, suggesting that the locus of high
exhumation has migrated northward. Although surface processes influence exhumation rates,
they do not necessarily engage in a feedback that sets the location of tectonic deformation.
The topography of mountain ranges results from the interplay between climate, tectonics, and surface processes (1). A key aspect of this interplay is considered to be that surface pro- cesses may influence the dynamics of actively
deforming mountain ranges through a system
of positive feedbacks involving tectonics and
erosion [reviewed in (2)]. The efficacy of such a
system has been emphasized in analog and nu-
merical experiments (3–5), which predict that
erosion, rather than tectonics, can control the locus
of deformation and exhumation of rocks toward
Earth’s surface (6). However, field evidence that
supports such models is mostly circumstantial
(5–13) and is based on the observation of a spatial
coincidence between rugged topography, high
rates of rock uplift, high precipitation, high stream
1Institute of Earth Surface Dynamics, University of Lausanne,
CH-1015 Lausanne, Switzerland. 2Institute of Geography,
University of Cologne, 50923 Cologne, Germany. 3Netherlands
Centre for Luminescence Dating and Soil Geography and
Landscape group, Wageningen University, Post Office Box 47,
6700 AA Wageningen, Netherlands.
*Corresponding author. Email: firstname.lastname@example.org