Physics – Quantum Physics
Scientific paper
2006-05-18
J. Phys. A: Math. Theor. 41, 025002 (2008).
Physics
Quantum Physics
10 pages, 9 figures
Scientific paper
10.1088/1751-8113/41/2/025002
In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the extensive properties of the thermal entropy $S($AB$)= S($A$)+S($B$)$ is violated. This observation motivates us to introduce the concept of correlation entropy between two points, as measured by mutual information in the information theory, to study the critical phenomena. A rigorous relation is established to display some drastic features of the non-vanishing correlation entropy of the subsystem formed by any two distant particles with long-range correlation. This relation actually indicates the universal role of the correlation entropy in understanding critical phenomena. We also verify these analytical studies in terms of two well-studied models for both the thermal and quantum phase transitions: two-dimensional Ising model and one-dimensional transverse field Ising model. Therefore, the correlation entropy provides us with a new physical intuition in critical phenomena from the point of view of the information theory.
Gu Shi-Jian
Lin Hai-Qing
Sun Chang-Pu
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