• Open Access

Assessing the Nonequilibrium Thermodynamics in a Quenched Quantum Many-Body System via Single Projective Measurements

L. Fusco, S. Pigeon, T. J. G. Apollaro, A. Xuereb, L. Mazzola, M. Campisi, A. Ferraro, M. Paternostro, and G. De Chiara
Phys. Rev. X 4, 031029 – Published 19 August 2014

Abstract

We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
1 More
  • Received 28 April 2014

DOI:https://doi.org/10.1103/PhysRevX.4.031029

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

L. Fusco1, S. Pigeon1, T. J. G. Apollaro2,1, A. Xuereb1,3, L. Mazzola1, M. Campisi4, A. Ferraro1, M. Paternostro1, and G. De Chiara1

  • 1Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen’s University, Belfast BT7 1NN, United Kingdom
  • 2Dipartimento di Fisica, Università della Calabria, 87036 Arcavacata di Rende (CS), Italy
  • 3Department of Physics, University of Malta, Msida MSD 2080, Malta
  • 4NEST, Scuola Normale Superiore & Istituto di Nanoscienze-CNR, I-56126 Pisa, Italy

Popular Summary

Nonequilibrium thermodynamics deals with the properties of physical, chemical, and biological systems that are not in thermodynamic equilibrium and the transformations that involve them. Fundamental fluctuation theorems have been formulated to relate fluctuations of physical quantities for nonequilibrium systems (such as work) to their equilibrium features. These relations can be exported to the quantum domain, where they play key roles in understanding the thermodynamic consequences of physically interesting processes occurring at the microscopic level. However, the general lack of direct observability in the quantum domain of thermodynamically important quantities hinders the collection and interpretation of data. We study in detail the conditions that a quantum mechanical process should satisfy in order to guarantee the direct accessibility, and thus the measurability, of work.

We apply our framework to the statistical features of the work done on or by a quantum many-body system and seek to understand the onset of quantum criticality by analyzing out-of-equilibrium dynamics. Our goal is to link nonequilibrium thermodynamics and macroscopically observable properties of a system. To this end, we employ sudden thermal quenching, which is decidedly nonadiabatic. Interestingly, the general noncommutative nature of Hamiltonians describing quantum processes turns out to be key for the direct observation of work in such systems. Our findings suggest that it is possible to observe signatures of quantum many-body criticality in the statistical moments of work.

We expect that our findings will be valuable for developing an experimentally certifiable framework of finite-time thermodynamics in quantum systems, which will be crucial for applications in nanotechnology and quantum technology.

Key Image

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 4, Iss. 3 — July - September 2014

Subject Areas
Reuse & Permissions

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×