Abstract
We review numerous applications of relative entropy estimates in Statistical Mechanics and Field Theory.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
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
Albeverio, S., Hoegh-Krohn, R., (1977): Dirichlet forms and diffusion processes on rigged Hilbert spaces, Z. Wahr. und verw. Geb. 40, 1–57
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
Bodineau, T., Zegarliński, B., (1998): Hypercontractivity via Spectral Theory, IC Preprint
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
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
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
Federbush, P., (1969): A partially alternative derivation of a result of Nelson, J. Math. Phys 10, 50–52
Glimm, J., Jaffe, A., (1987): Quantum Physics: The functional integral point of view, Springer-Verlag
Gross, L., (1976): Logarithmic Sobolev inequalities, Amer. J. Math. 97, 1061–1083
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
Herbst, I., (1976): On Canonical Quantum Field Theories, J. Math. Phys. 17, 1210–1221
Lu, S.L., Yau, H.T., (1993): Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics. Commun. Math. Phys. 156, 399–433
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
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
Minlos, R.A., (1996): Invariant subspaces of the stochastic Ising high temperature dynamics, Markov Process and Rel. Fields 2, no. 2, 263–284
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
Ogielski, A.T., (1985): Dynamics of three dimensional Ising spin glasses in thermal equilibrium, Phys. Rev. B32, No 11 7384
Olkiewicz, R., Zegarliński, B., (1999): Hypercontractivity In Noncommutative ILp Spaces. J. Funct. Anal. 161, 246–285
Simon, B., (1974): The P(φ)2 Euclidean (Quantum) Field Theory, Princeton Univ Press
Stroock, D.W., Zegarliński, B., (1992): The Logarithmic Sobolev inequality for Continuous Spin Systems on a Lattice, J. Funct. Anal. 104, 299–326
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
Stroock, D.W., Zegarliński, B., (1992): The Logarithmic Sobolev inequality for Discrete Spin Systems on a Lattice, Commun. Math. Phys. 149, 5–193
Stroock, D.W., Zegarliński, B., (1995): The Ergodic Properties of Glauber Dynamics, J. Stat. Phys. 81, 1007–1019
Zegarliński, B., (1990): On log-Sobolev Inequalities for Infinite Lattice Systems, Lett. Math. Phys. 20, 173–182
Zegarliński, B., (1990): Log-Sobolev Inequalities for Infinite One Dimensional Lattice Systems, Commun. Math. Phys. 133, 147–162
Zegarliński, B., (1992): Dobrushin Uniqueness Theorem and Logarithmic Sobolev Inequalities, J. Funct. Anal. 105, 77–111
-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
Zegarliński, B., (1998): All that is Sobolev Inequality, IC Preprint
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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