Note on entropy dynamics in the Brownian SYK model

Abstract We study the time evolution of Rényi entropy in a system of two coupled Brownian SYK clusters evolving from an initial product state. The Rényi entropy of one cluster grows linearly and then saturates to the coarse grained entropy. This Page curve is obtained by two different methods, a path integral saddle point analysis and an operator dynamics analysis. Using the Brownian character of the dynamics, we derive a master equation which controls the operator dynamics and gives the Page curve for purity. Insight into the physics of this complicated master equation is provided by a complementary path integral method: replica diagonal and non-diagonal saddles are responsible for the linear growth and saturation of Ŕenyi entropy, respectively.

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Subsystem Rényi entropy of thermal ensembles for SYK-like models

SciPost Physics ◽

10.21468/scipostphys.8.6.094 ◽

2020 ◽

Vol 8 (6) ◽

Cited By ~ 2

Author(s):

Pengfei Zhang ◽

Chunxiao Liu ◽

Xiao Chen

Keyword(s):

Path Integral ◽

Exact Diagonalization ◽

Renyi Entropy ◽

Rényi Entropy ◽

Integral Formalism ◽

Fermionic Model ◽

Random Interactions ◽

Thermal Entropy ◽

Kitaev Model ◽

Infinite Range

The Sachdev-Ye-Kitaev model is an NN-modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large-NN limit. The results are consistent with exact diagonalization and can be well approximated by thermal entropy with an effective temperature when subsystem size M\leq N/2M≤N/2. We also consider generalizations of the SYK model with quadratic random hopping term or U(1)U(1) charge conservation.

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Path Integral Method in the Mean-field Model for the Magnetic Vector Potential

Geomagnetism and Aeronomy ◽

10.1134/s0016793220070300 ◽

2020 ◽

Vol 60 (7) ◽

pp. 989-992

Author(s):

E. V. Yushkov ◽

C. R. Kamaletdinov ◽

D. D. Sokoloff

Keyword(s):

Path Integral ◽

Vector Potential ◽

Integral Method ◽

Field Model ◽

Mean Field ◽

Magnetic Vector Potential ◽

Magnetic Vector ◽

Mean Field Model ◽

The Mean ◽

Path Integral Method

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Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

Journal of High Energy Physics ◽

10.1007/jhep12(2020)160 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Jiaju Zhang ◽

M.A. Rajabpour

Keyword(s):

Excited States ◽

Single Particle ◽

Renyi Entropy ◽

Rényi Entropy ◽

Large Momentum ◽

Particle State ◽

Two Dimensional ◽

Universal Form ◽

Conformal Field ◽

Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

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Testing homogeneity of the galaxy distribution in the SDSS using Renyi entropy

Journal of Cosmology and Astroparticle Physics ◽

10.1088/1475-7516/2021/07/019 ◽

2021 ◽

Vol 2021 (07) ◽

pp. 019

Author(s):

Biswajit Pandey ◽

Suman Sarkar

Keyword(s):

Renyi Entropy ◽

Rényi Entropy ◽

Galaxy Distribution ◽

The Galaxy ◽

Testing Homogeneity

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Conditional Rényi Entropy and the Relationships between Rényi Capacities

Entropy ◽

10.3390/e22050526 ◽

2020 ◽

Vol 22 (5) ◽

pp. 526

Author(s):

Gautam Aishwarya ◽

Mokshay Madiman

Keyword(s):

Mutual Information ◽

Renyi Entropy ◽

Rényi Entropy ◽

Basic Properties ◽

Reference Measure ◽

Definition Of ◽

Discrete Setting

The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored.

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