Foundations of statistical mechanics from symmetries of entanglement

Deffner, Sebastian; Zurek, Wojciech H.

doi:10.1088/1367-2630/18/6/063013

Cited by 30 publications

(32 citation statements)

References 23 publications

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“…Given the success of this derivation of Born's rule, it is then natural to inquire whether equilibrium in an individual quantum system can be defined without appeal to ensembles, but, rather, by recognizing symmetries of entanglement with its heat bath. I review this approach [10] with the focus on the demand that equilibrium should represent the absence of motion in an individual system. The main result establishes that any unitary evolution operator acting on a state representing microcanonical equilibrium that results from entanglement with the environment can be "undone" in the composite state that represents both the system and the environment by a suitable "counter-evolution" in the environment.…”

Section: Introductionmentioning

confidence: 99%

Eliminating ensembles from equilibrium statistical physics: Maxwell’s demon, Szilard’s engine, and thermodynamics via entanglement

Zurek

2018

Physics Reports

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A system in equilibrium does not evolve -time independence is its telltale characteristic. However, in Newtonian physics the microstate of an individual system (a point in its phase space) evolves incessantly in accord with its equations of motion. Ensembles were introduced in XIX century to bridge that chasm between continuous motion of phase space points in Newtonian dynamics and stasis of thermodynamics: While states of individual classical systems inevitably evolve, a phase space distribution of such states -an ensemble -can be time-independent. I show that entanglement (e.g., with the environment) can yield a time-independent equilibrium in an individual quantum system. This allows one to eliminate ensembles -an awkward stratagem introduced to reconcile thermodynamics with Newtonian mechanics -and use an individual system interacting and therefore entangled with its heat bath to represent equilibrium and to elucidate the role of information and measurements in physics. Thus, in our quantum Universe one can practice statistical physics without ensembles -hence, in a sense, without statistics. The elimination of ensembles uses ideas that led to the recent derivation of Born's rule from the symmetries of entanglement, and I start with a review of that derivation. I then review and discuss difficulties related to the reliance on ensembles and illustrate the need for ensembles with the classical Szilard's engine. A similar quantum engine -a single system interacting with the thermal heat bath environment -is enough to establish thermodynamics. The role of Maxwell's demon (which in this quantum context resembles Wigner's friend) is also discussed.

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Section: Introductionmentioning

confidence: 99%

Eliminating ensembles from equilibrium statistical physics: Maxwell’s demon, Szilard’s engine, and thermodynamics via entanglement

Zurek

2018

Physics Reports

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“…In other words, the momentum is invariance at every single time. This leads us to a concept called envariance (environment assisted invariance) a discovered symmetry in the non-local quantum state [18] which later known as entanglement assisted invariance [19].…”

Section: Discussionmentioning

confidence: 99%

Invariance in Transverse Momentum of Photons in Double-slit Experiment

Rahim

Kamal

Othman

2018

JST

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“…We stress that the assumption (8) does not require the global system to be in a Gibbs state. It holds for almost all global pure states chosen from a given energy shell [36,37], and it is always satisfied for almost any time if the global Hamiltonian satisfies the Eigenstate Thermalization Hypothesis [26,] (see also [68]).…”

Section: Universal Localitymentioning

confidence: 99%

Universal locality of quantum thermal susceptibility

2017

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The ultimate precision of any measurement of the temperature of a quantum system is the inverse of the local quantum thermal susceptibility [De Pasquale et al., Nature Communications 7, 12782 (2016)] of the subsystem with whom the thermometer interacts. If this subsystem can be described with the canonical ensemble, such quantity reduces to the variance of the local Hamiltonian, that is proportional to the heat capacity of the subsystem. However, the canonical ensemble might not apply in the presence of interactions between the subsystem and the rest of the system. In this work we address this problem in the framework of locally interacting quantum systems. We prove that the local quantum thermal susceptibility of any subsystem is close to the variance of its local Hamiltonian, provided the volume to surface ratio of the subsystem is much larger than the correlation length. This result greatly simplifies the determination of the ultimate precision of any local estimate of the temperature, and rigorously determines the regime where interactions can affect this precision

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Foundations of statistical mechanics from symmetries of entanglement

Cited by 30 publications

References 23 publications

Eliminating ensembles from equilibrium statistical physics: Maxwell’s demon, Szilard’s engine, and thermodynamics via entanglement

Eliminating ensembles from equilibrium statistical physics: Maxwell’s demon, Szilard’s engine, and thermodynamics via entanglement

Invariance in Transverse Momentum of Photons in Double-slit Experiment

Universal locality of quantum thermal susceptibility

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