Modified Entropic Force
高长军
中国科学院国家天文台
 I. Introduction
 II. Modified Newtonian Gravity
 III. Modified Friedmann equation
 IV. Conclusion and discussion
Classical Black Holes
T 0
只吸收物质,不辐射物质,冷冰冰的.
Quantum Black holes
T  0
黑洞既吸收物质,又辐射物质, 热腾腾的.
 考虑到量子力学, 黑洞满足热力学四
定律, 这样, 黑洞完全成了一个热力
学系统. 推而广之, 不只是黑洞, 任
何一个引力系统都与一个热力学系统
相对应.
1. Using the Causius relation and equiveverlece principle, Jacobson derived the Einstein
equations in 1995.
2. Using the equipartition law of energy and a thermodynamic relation, Padmanabhan derived
the Newtonian Gravity in 2009.
3. This year, Verlinde proposed an interesting idea that gravity may be not fundamental but can
be interpreted as an entropic force. The entropic force is caused by the changes of the
information associated with the system. Using the equipartition law of energy and holographic
principle, he obtains the Newtonian gravity.
Entropic Force
dE  Fdx
dE  TdS
S
F T
x
1
c 6
T 

8M kG
黑洞把引力论，相对论，热力
学和量子力学联系了起来。

In their derivations, the equipartition law of energy is important.
能量按自由度均分和弹性波

Newtonian Gravity
 考虑一个球形的空间区域，面积为A. 球内的总的自由度为N

球内有物质分布，因此在给定半径处具有引力场强 g。根据Unruh效应，
该引力场强对应一个温度为 T 的热辐射，我们有
 由能量均分定理，系统内总的能量为
所以

Modified Newtonian Gravity

When x approaches infinity
 General Relativity is the strong field extension of
Newtonian gravity.
 This model is the weak field extension of
Newtonian gravity.

1
1
1
, 3 , 4 ,   
2
r
r
r
1
1
1
, 1 , 1/ 2 .
2
r
r
r
 Modified Poisson’s equation
15
g D  10 N  kg
1
Different from MOND theory
  D  4

x

2
1

x

x

D
1 x

3
x


1 
1  
3


g
x
gD
 III. Cosmology
Friedmann equation


When
x  1,
we have the Friedmann equation in GR;
Conclusion and discussion
1. Using the Debye model, we find the cosmic acceleration can be interpreted without
invoking dark energy.
2. In the Solar system and Galaxy scales, the model can be very well approximated as
Newtonian gravity.
3. This Debye model is for three dimensional. How about for one dimensional and two
dimensional Debye model? Holographic principle reveals that two dimensional
Debye model seems much reasonable.
4. The Poisson’s equation is derived. The how to derive the corresponding Einstein
equations from the variation principle?
5. How to derive this model from the specific microscopic structure of space-time?
Two dimensional Debye model:

2
D 
2
x

0
y2
dy
y
e 1
One dimensional Debye model:
1
D
x


x

x

x
0
y
dy
y
e 1
n dimensional Debye model:
1
D n
x
0
yn
dy
y
e 1
德拜模型（理论泡沫？）
迪拜模式（房产泡沫！）
谢谢！