TY - GEN

T1 - Thermodynamic network analysis with quantum spin statistics

AU - Wang, Jianjia

AU - Wilson, Richard C.

AU - Hancock, Edwin R.

N1 - Publisher Copyright:
© Springer International Publishing AG 2016.

PY - 2016

Y1 - 2016

N2 - In this paper, we explore the thermodynamic analysis of networks using a heat-bath analogy and different choices of quantum spin statistics for the occupation of energy levels defined by the network. We commence from the set of energy states given by the eigenvalues of the normalized Laplacian matrix, which plays the role of the Hamiltonian operator of the network. We explore a heat bath analogy in which the network is in thermodynamic equilibrium with a heat-bath and its energy levels are occupied by either indistinguishable bosons or fermions obeying the Pauli exclusion principle. To compute thermodynamic characterization of this system, i.e. the entropy and energy, we analyse the partition functions relevant to Bose-Einstein and Fermi-Dirac statistics. At high temperatures, the effects of quantum spin statistics are disrupted by thermalisation and correspond to the classical Maxwell-Boltzmann case. However, at low temperatures the Bose-Einstein system condenses into a state where the particles occupy the lowest energy state, while in the Fermi-Dirac system there is only one particle per energy state. These two models produce quite different entropic characterizations of network structure, which are appropriate to different types of structure. We experiment with the two different models on both synthetic and real world imagery, and compare and contrast their performance.

AB - In this paper, we explore the thermodynamic analysis of networks using a heat-bath analogy and different choices of quantum spin statistics for the occupation of energy levels defined by the network. We commence from the set of energy states given by the eigenvalues of the normalized Laplacian matrix, which plays the role of the Hamiltonian operator of the network. We explore a heat bath analogy in which the network is in thermodynamic equilibrium with a heat-bath and its energy levels are occupied by either indistinguishable bosons or fermions obeying the Pauli exclusion principle. To compute thermodynamic characterization of this system, i.e. the entropy and energy, we analyse the partition functions relevant to Bose-Einstein and Fermi-Dirac statistics. At high temperatures, the effects of quantum spin statistics are disrupted by thermalisation and correspond to the classical Maxwell-Boltzmann case. However, at low temperatures the Bose-Einstein system condenses into a state where the particles occupy the lowest energy state, while in the Fermi-Dirac system there is only one particle per energy state. These two models produce quite different entropic characterizations of network structure, which are appropriate to different types of structure. We experiment with the two different models on both synthetic and real world imagery, and compare and contrast their performance.

KW - Network entropy

KW - Quantum spin statistics

UR - http://www.scopus.com/inward/record.url?scp=84996656530&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-49055-7_14

DO - 10.1007/978-3-319-49055-7_14

M3 - Conference Proceeding

AN - SCOPUS:84996656530

SN - 9783319490540

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 153

EP - 162

BT - Structural, Syntactic, and Statistical Pattern Recognition - Joint IAPR International Workshop S+SSPR 2016, Proceedings

A2 - Biggio, Battista

A2 - Wilson, Richard

A2 - Loog, Marco

A2 - Escolano, Francisco

A2 - Robles-Kelly, Antonio

PB - Springer Verlag

T2 - Joint IAPR International Workshops on Structural and Syntactic Pattern Recognition, SSPR 2016

Y2 - 29 November 2016 through 2 December 2016

ER -