Skip to main content

Relative Entropy Estimates in Statistical Mechanics and Field Theory

  • Conference paper
  • First Online:
Theoretical Physics Fin de Siècle

Part of the book series: Lecture Notes in Physics ((LNP,volume 539))

  • 372 Accesses

Abstract

We review numerous applications of relative entropy estimates in Statistical Mechanics and Field Theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Araki, H., (1960): Hamiltonian formalisms and the canonical commutation relations in quantum field theory, J. Math. Phys. 1, 492–504

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Albeverio, S., Hoegh-Krohn, R., (1977): Dirichlet forms and diffusion processes on rigged Hilbert spaces, Z. Wahr. und verw. Geb. 40, 1–57

    Article  MATH  MathSciNet  Google Scholar 

  • Bakry, D., Emery, M., (1984): Hypercontractivitè de semi-groupes des diffusion, C.R. Acad. Sci. Paris Ser. I 299 pp. 775–777; Diffusions hypercontractives, pp 177–206 in Sem. de Probabilites XIX, Azema J. and Yor M. (eds.), LNM 1123

    Google Scholar 

  • Bodineau, T., Zegarliński, B., (1998): Hypercontractivity via Spectral Theory, IC Preprint

    Google Scholar 

  • Carlen, E.A., Stroock, D.W., (1986): An application of the Bakry-Emery criterion to infinite dimensional diffusions, Sem.de Probabilites XX, Azema J. and Yor M. (eds.), LNM 1204, pp, 341–348

    Google Scholar 

  • Cesi, F., Maes, C., Martinelli, F., (1997): Relaxation to equilibrium for two dimensional disordered Ising systems in the Griffths phase, Commun. Math. Phys. 189, 323–335

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Dobrushin, R.L., Shlosman, S., (1985): Completely analytical Gibbs fields, pp. 371–403 in Statistical Physics and Dynamical Systems, Rigorous Results, Eds. Fritz, Jaffe and Szasz, Birkhäuser Completely analytical interactions: constructive description, (1987): J. Stat. Phys. 46, 983–1014

    Google Scholar 

  • Federbush, P., (1969): A partially alternative derivation of a result of Nelson, J. Math. Phys 10, 50–52

    Article  MATH  ADS  Google Scholar 

  • Glimm, J., Jaffe, A., (1987): Quantum Physics: The functional integral point of view, Springer-Verlag

    Google Scholar 

  • Gross, L., (1976): Logarithmic Sobolev inequalities, Amer. J. Math. 97, 1061–1083

    Article  MATH  ADS  Google Scholar 

  • Guionnet, A., Zegarliński, B., (1996): Decay to Equilibrium in Random Spin Systems on a Lattice, Commun. Math. Phys. 181, 703–732; Decay to Equilibrium in Random Spin Systems on a Lattice, II, J. Stat. Phys. 86, (1997) 899–904

    Article  MATH  ADS  Google Scholar 

  • Herbst, I., (1976): On Canonical Quantum Field Theories, J. Math. Phys. 17, 1210–1221

    Article  ADS  MathSciNet  Google Scholar 

  • Lu, S.L., Yau, H.T., (1993): Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics. Commun. Math. Phys. 156, 399–433

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Majewski, A.W., Olkiewicz, R., Zegarliński, B., (1998): Construction and Ergodicity of Dissipative Dynamics for Quantum Spin Systems on a Lattice, J. Phys. A31, 2045–2056

    ADS  Google Scholar 

  • Martinelli, F., Olivieri, E., (1994): Approach to Equilibrium of Glauber Dynamics in the One Phase Region: I. The Attractive case/ II. The General Case. Commun. Math. Phys. 161, 447–486 / 487–514

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Minlos, R.A., (1996): Invariant subspaces of the stochastic Ising high temperature dynamics, Markov Process and Rel. Fields 2, no. 2, 263–284

    MATH  MathSciNet  Google Scholar 

  • Minlos, R.A., Trishch, A.G., (1994): The complete spectral decomposition of a generator of Glauber dynamics for the one-dimensional Ising model, Uspekhi Mat. Nauk 49, no. 6(300), 210–211

    MATH  MathSciNet  Google Scholar 

  • Ogielski, A.T., (1985): Dynamics of three dimensional Ising spin glasses in thermal equilibrium, Phys. Rev. B32, No 11 7384

    ADS  Google Scholar 

  • Olkiewicz, R., Zegarliński, B., (1999): Hypercontractivity In Noncommutative ILp Spaces. J. Funct. Anal. 161, 246–285

    Article  MATH  MathSciNet  Google Scholar 

  • Simon, B., (1974): The P(φ)2 Euclidean (Quantum) Field Theory, Princeton Univ Press

    Google Scholar 

  • Stroock, D.W., Zegarliński, B., (1992): The Logarithmic Sobolev inequality for Continuous Spin Systems on a Lattice, J. Funct. Anal. 104, 299–326

    Article  MATH  MathSciNet  Google Scholar 

  • Stroock, D.W., Zegarliński, B., (1992): The Equivalence of the Logarithmic Sobolev Inequality and the Dobrushin-Shlosman Mixing Condition, Commun. Math. Phys. 144, 303–323

    Article  MATH  ADS  Google Scholar 

  • Stroock, D.W., Zegarliński, B., (1992): The Logarithmic Sobolev inequality for Discrete Spin Systems on a Lattice, Commun. Math. Phys. 149, 5–193

    Article  Google Scholar 

  • Stroock, D.W., Zegarliński, B., (1995): The Ergodic Properties of Glauber Dynamics, J. Stat. Phys. 81, 1007–1019

    Article  MATH  ADS  Google Scholar 

  • Zegarliński, B., (1990): On log-Sobolev Inequalities for Infinite Lattice Systems, Lett. Math. Phys. 20, 173–182

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Zegarliński, B., (1990): Log-Sobolev Inequalities for Infinite One Dimensional Lattice Systems, Commun. Math. Phys. 133, 147–162

    Article  ADS  MATH  Google Scholar 

  • Zegarliński, B., (1992): Dobrushin Uniqueness Theorem and Logarithmic Sobolev Inequalities, J. Funct. Anal. 105, 77–111

    Article  MATH  MathSciNet  Google Scholar 

  • -Zegarliński, B., (1995): Ergodicity of Markov Semigroups, pp. 312–337, in Proc. of the Conference: Stochastic Partial Differential Equations, Edinburgh 1994, Ed. A. Etheridge, LMS Lec. Notes 216, Cambridge University Press

    Google Scholar 

  • Zegarliński, B., (1998): All that is Sobolev Inequality, IC Preprint

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zegarliński, B. (2000). Relative Entropy Estimates in Statistical Mechanics and Field Theory. In: Borowiec, A., Cegła, W., Jancewicz, B., Karwowski, W. (eds) Theoretical Physics Fin de Siècle. Lecture Notes in Physics, vol 539. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46700-9_10

Download citation

  • DOI: https://doi.org/10.1007/3-540-46700-9_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66801-5

  • Online ISBN: 978-3-540-46700-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics