entropy 存量 stock gdp是衡量经济状况的比较标准，主要有存量和变量两大部分，而变量又可分为换量和增量。

mitchell porter

mitchell porter 784

When Erik Verlinde talks about "entropy" and "temperature", you should put those words in mental quotation marks. "Entropy" really means "phase space volume", and "temperature" means "density of energy levels". It's just that the relationships between these quantities resemble the relationships in thermodynamics. Only on or behind a gravitational horizon, such as inside a black hole, does it truly become thermodynamics.

His idea is best understood in terms of the matrix realization of string theory. The diagonal matrix elements represent the position in space of D-branes, and the off-diagonal matrix elements represent the open strings between the D-branes.

Suppose you have some D-branes which make up a black hole; they will be described by some part of the matrix diagonal, and there will be a sub-matrix of off-diagonal matrix entries connecting them. In this case, the off-diagonal degrees of freedom will be about the same size as the on-diagonal degrees of freedom. This is the thermodynamic equilibrium, equilibrium between off-diagonal and on-diagonal.

Outside a black hole, it's different. The off-diagonal elements are close to zero. This holds both for off-diagonal elements between two D-branes in space, and for off-diagonal elements between a D-brane inside a black hole and another D-brane outside it.

His claim is that gravity is an effective force which you see happening on the matrix diagonal - acting on the positions of matter in space - which is just an approximation to the full matrix dynamics. The full matrix is evolving according to some matrix-model Hamiltonian through the abstract space of matrix values. Because it is Hamiltonian dynamics, there is conservation of phase-space volume. But if you just focus on the on-diagonal degrees of freedom, and construct an approximate dynamics by integrating out the off-diagonal elements, you will find some effective forces acting on the on-diagonal degrees of freedom (positions of matter in space). Technically, they are adiabatic reaction forces. Adiabatic processes are slow, and the on-diagonal degrees of freedom change slowly compared to the off-diagonal degrees of freedom. The conservation of phase space volume in the full dynamical system becomes the presence of a reaction force acting on the slow variables in the approximation; this is a general principle that was explored in some depth by the physicist Michael Berry. Verlinde is applying this to matrix theory.

Gravity is the leading effect, but all the other forces are supposed to be reaction forces too, higher-order corrections to the reduced dynamics of the on-diagonal degrees of freedom.

There's no paper spelling this out yet, but it's in his talk at Strings 2011.

In matrix theory, you aren't working in space-time any more. You have a matrix which evolves in time, and events in ordinary space correspond to what happens on the matrix diagonal. In AdS/CFT, on the other hand, you still have space and time on the boundary, just with fewer dimensions than in the bulk. So that is the first bridge to be crossed.

Now what about the holographic screens? In Verlinde's idea, the entropy is not on the screens. All the actual entropy (the matrix "entropy", anyway) is behind the gravitational horizons. "Entropy" (volume in matrix phase space) is an adiabatic invariant for the reduced dynamics of the matrix diagonal, and an adiabatic invariant is a quantity that doesn't change. Matter in space attracts other matter because of the underlying matrix dynamics. Distance from a screen (such as the equipotential surfaces he considers in his 2010 paper) is a relationship between on-diagonal degrees of freedom, and it's connected to these pseudo-thermodynamic quantities "entropy" and "temperature" (see my first paragraph), but matrix "entropy" isn't located outside the black holes and isn't changing outside the black holes.

The holographic screens really apply at a level of description above the matrix level employed by Verlinde - Bousso's "covariant entropy bound". This is a statement that the entropy of matter along lightlike surfaces is bounded by A/4G. This must have something to do with black holes forming if you get too much matter together - Bousso's bound is the entropy for a black hole with surface area A - but he says the origin of the general bound is obscure and should arise from a principle of quantum gravity, such as the holographic principle.

As I said, in AdS/CFT you still have space and time, you just have less space dimensions on the boundary. At the end of his talk linked above, Bousso discusses holographic screens in the AdS bulk. The bound applies in AdS space, but here you can understand it in terms of the boundary theory; the entropy in the bulk corresponds to the entropy in the boundary CFT, and introducing a screen in the bulk corresponds to introducing a cutoff on the boundary CFT. Moving the screen out to the boundary at infinity corresponds to removing the cutoff in the CFT. So in AdS space, there is a CFT corresponding to a holographic screen: a cutoff version of the full boundary CFT.

In other spaces (that are not anti de Sitter), we don't have the gauge/gravity duality worked out - we don't know the boundary CFT - and so we don't know the cutoff appropriate for a screen in the middle of the bulk space, either. But it seems likely that when we do have the counterpart to AdS/CFT for other spaces (flat space, de Sitter space,...) figured out, it will be possible to define regularizations of the underlying CFT which correspond to specific holographic screens in the bulk.

To fully realize Erik Verlinde's argument in the context of AdS/CFT, the boundary CFT would need to be derived from a matrix model. I'm not sure of the status of that line of research, but the other Verlinde brother, Herman, has a paper constructing a twistor matrix model for N=4 Yang-Mills, the boundary CFT for Type IIB strings in AdS5 x S5. So it might be explored in that context.

For the real world, we want dS/CFT, with time holographically emergent from a Euclidean CFT at past infinity. Some of us are waiting anxiously for a paper by Hartman and Anninos, promised at Strings 2011, which will finally provide a detailed example of dS/CFT, ten years after Andrew Strominger first described how it should work in principle. One of the issues awaiting resolution is that in de Sitter space, you have, not just black-hole event horizons, but observer-dependent cosmological horizons. "Behind the horizon" - which in Verlinde's scheme is where the on-diagonal/off-diagonal thermodynamic equilibrium is realized - should correspond to beyond the cosmological horizon. But that space should be just like space here - unlike the space inside a black hole. So there are major unanswered questions. My guess is that cosmological horizons in de Sitter space are more like mid-bulk holographic screens and that the matrix "entropy" isn't there, it's at the boundary at past infinity. I also guess that this has something to do with the state of the universe before inflation being something like the state of the universe inside a black hole - it's a place where off-diagonal and on-diagonal degrees of freedom are in equilibrium, and the usual description of space does not apply. But those are just guesses.

 

现象派经济学 [ hullo ] 于:2014-05-05 08:12:18 复:4006045

看了陈经先生的帖子，原本想写一些不同意见的帖子，没想到那么多人献花宝推。陈经的观点与罗化生的观点类似，都是鼓吹投资，但罗化生的帖子并没有得多少花，为什么会这样的呢？
俺的理解是两个原因造成的，一是陈罗二人在河里的名声地位决定的，二是陈经先生用的是现象分析法，而罗化生是用比较分析法。
现象派的威力的确太大了，理论体系的分析，实例的比较分析，都不如现象分析，更直观，更有煽动力。
社会达尔文主义，唯意志论，现象派，在河里很盛行，当然，在全社会都很盛行，叔本华的作为意志和表象的世界，真是恰如其分，社会达尔文主义的根本是客观意志，唯意志论的根本是主观意志，现象派的基础是表象，其性质都是相似的，都是用简单直观的表象和意志，来认识世界。
gdp是衡量经济状况的比较标准，主要有存量和变量两大部分，而变量又可分为换量和增量。
典型的例子就是汽车，保有量，增长量，替换量，就能很好地说明gdp的构成。美国的汽车保有量大约是2.5亿辆，年销售量大约是1500万辆，增长量基本为零，1500万辆基本为替换量。中国的汽车保有量大约是1.2辆左右，年销售量大约在2000万辆左右，替换量应该不足500万辆，也就是年增长量在1500万辆以上。
即使不考虑中国和美国的进出口问题，只是根据存量，换量，增量来分析，也是中国经济的水分多，而美国的水分少，因为，存量都是实实在在的财富，换量的成本也很低，而且比增量更稳定。
竟然将维持存量的经济活动，视为“中间环节”，“互动环节”，而只强调变量，怎是太表象化了。
发达国家的第三产业，占gdp的比重很大，主要是因为存量很大造成的，而缺少积累形成的存量，而大谈发展第三产业，要么是空中楼阁，要么是印度那种人身依附的怪胎经济。
存量决定财富，是经济活动的目的，变量决定发展，是经济活动的手段，鼓吹大投资的现象派经济学，完全本末倒置。
因为，无效率的大投资，大多时候并不会创造财富，而只是在转移财富，造成社会两极分为，又进一步影响社会的稳定与发展。
财富创造，与财富转移，是经济活动的两个主要方面，如果是财富创造，大于财富转移，就是有效率的，倘若财富转移，大于财富创造，就是无效率的。
中国现在的投资，大部分已经是财富转移，大于财富创造，现在还鼓吹大投资，说是别有用心，在这个小众论坛里，只怕未必，主要应该是陷入了表象的迷幻里。
存量，变量，财富创造，财富转移，这是衡量经济活动的基本标准，现在中国的唯gdp论，根本的目的，不是为了财富创造，而是权富们为了财富转移。
做大存量，财富创造，才是经济发展的根本，而为了发展而发展，只不过是财富转移的障眼法。
家门口的一条沥青路，没几年就破败不堪了，后来，变成了水泥路，还以为能用上十几年，没想到只一个冬天，上面的就完全开裂了，春风一吹，就是一阵水泥灰。
离家不远的一条宽阔马路，车辆并不多，路况也较好，去年不知为啥，竟然重修，路两边的红色水泥砖人行道，几乎没人走，也都换上了人造石头的。
修了几个公园，多是人迹罕至的地方，俺母亲都知道，不乱修乱建，怎么方便贪腐呀，总不能直接将公款搬回家吧。
大投资，呵呵，钱是从天上掉下来的么？企业的利润，应该是投资的主要来源，但中国的投资主体，并不主要是企业，而是政府，政府的钱从哪里来的？
税费，卖地，借贷，是政府投资的主要资金来源，前两者主要来自中下阶层，借贷主要要将来偿还，无论任何国家，政府投资都是效率低下，贪腐严重的。
政府投资，最大的好处是时间成本低，即使路修了，质量太差，又要重修，也比难以修建要好，因为，资源的浪费，总比生命的浪费要好。
政府投资，导致的财富转移，在中国还有另一个好处，就如给公务员加薪，借钱给美国消费，增加了国内的消费能力，因为，毛泽东时代，造成的人人差不多，生产可以外资，民资，国资一起上，但消费的提高，却是源自积累，因此，财富转移尽管十分不公平，但也促进了经济的发展。
但到了今天，权富阶层大量买奢侈品，豪华轿车，购置更多的房产，已经难以促进消费，甚至抬高了房价，租金，反而严重抑制了正常消费，因此，原本不公平的财富转移，必须减少，那么造成财富转移的主要渠道，土地财政和大投资，就必须减少，必须规范。
因为政府掌控更多的资源和权力，基础建设投资的时间成本低，因此，腐败成本就是不得不付出的代价，但财富转移的有利方面，已经消失，再继续财富转移，只能将中国推向深渊，社会的阶层分裂，区域分化，不但是严重的经济问题，更是政治问题。