Mapping the economy to the some statistical physics models we get strong indications that, in contrary to the pure stock market, the stock market with derivatives could not self-regulate.
Deep Dive into Mapping markets to the statistical mechanics: the derivatives act against the self-regulation of stock market.
Mapping the economy to the some statistical physics models we get strong indications that, in contrary to the pure stock market, the stock market with derivatives could not self-regulate.
arXiv:0903.3254v1 [q-fin.GN] 18 Mar 2009
Mapping markets to the statistical mechanics: the derivatives act against the
self-regulation of stock market
David B. Saakian1,2,3
1Yerevan Physics Institute, Alikhanian Brothers St. 2, Yerevan 375036, Armenia
2Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan and
3National Center for Theoretical Sciences:Physics Division,
National Taiwan University, Taipei 10617, Taiwan
(Dated: October 29, 2018)
Mapping the economy to the some statistical physics models we get strong indications that, in
contrary to the pure stock market, the stock market with derivatives could not self-regulate.
Economics.
Statistical physics.
Money.
Energy.
Value.
Free energy.
The capitalization of stocks.
Work.
Volatility.
Local temperature.
Market’s Kolmogorov
Entropy
complexity.
Infinitely effective market.
Hamiltonian
Statistical mechanics.
Self-regulating real market.
Thermostat, 0-th law,2-nd
law of thermodynamics.
Accidental arbitrage.
Maxwell Demon.
Strong usage of derivatives,
Strong Born-Openheimer
crisis.
interaction [10], violation of
thermodynamic laws.
TABLE I: The correspondence between economics and sta-
tistical physics.
Introduction. How can we understand the crisis? Shall
we revise the whole economic theory of highly effective
self-regulating market with ”infinitely rational agents” in
favor of more modern theories (behaviorial economics”)?
Our idea is that there is no need for a radical change in
economic theory. We should just borrow more ideas from
statistical physics, and the reflection concept of Marxist
philosophy.
In recent decades it has been well realized that some
aspects of financial markets could be analyzed well with
the methods of statistical physics, especially the idea of
scaling for the fat tails of distributions [1]. The scaling
is identified in statistical physics with the universality of
critical phenomena near the second order phase transi-
tion point. This rather technical approach was certainly
useful.
Nevertheless, statistical physics is much richer
discipline than only second order phase transition the-
ory.
In [2] has been observed the similarity of money
and free energy. V. P. Maslov identified the entropy of
market with its complexity [3], and I just borrow his idea
for the Table 1, giving the correspondence between sta-
tistical physics and economics.
A fruitful mapping of
the wealth distribution and international trade to ther-
modynamic has been done in [4, 5]. The thermodynamic
approach was very successful here, because in this narrow
field there is an equivalent of the first law (the conser-
vation of money). We are interested in a more general
situation.
In our article [6] we tried to identify different classes
of universality of complex systems, rather than consider
only the second order phase transitions. One can use sev-
eral variables to identify the universality class (the sys-
tems from the same class should share the same criteria):
a. The subdominant behavior of free energy or some en-
tropy; b. intrinsic information -theoretical aspects (het-
erogeneity of agents,
ferromagnetic-antiferromagnetic
couplings, gauge invariance). These concepts could be
useful for investigation of simple markets.
Let as analyze the economics using the further ideas
borrowed from statistical physics and philosophy. In Ta-
ble 1, we give some correspondence between two areas.
The connection between the II law of thermodynamics
and no-arbitrage property of market is known. Perhaps
we should take Thomson’s formulation: it is impossible
get a work (income) from a system in the equilibrium.
A fundamental concept for analyzing any serious phe-
nomenon in physics and in interdisciplinary science is the
concept of reflection, well realized in the Marxist philos-
ophy.
There is an objective reality, identified sometimes with
the substance of materia, and its reflection- the subjec-
tive reality. It is not an abstract philosophical concept.
On the contrary, it is highly concrete and useful for ap-
plications in statistical physics.
Another concept we need, is an amount of motion in-
vented by philosophers De-Cartesius and Leibnitz. It has
been identified in classical mechanics first with momen-
tum, later with energy.
Statistical physics.
The reflection and amount of
motion are explicit in statistical physics. There is a hier-
archy of motions: at the background level - a microscopic
motion of molecules with some energy. This is an objec-
tive reality. The system quickly goes to some equilibrium
and it is possible to define the temperature (0-th law of
thermodynamic).
At the next level, we have a thermodynamics (with an
observer, as has been realized by W. Heisenberg) with
free energy. Using the idea of Gibbs, one calculates the
2
partition (a probability like quantity), then, taking its
logarithm, the free energy. The free energy is the man-
ageable amount of motion on a macroscopic level.
Advanced case. There are physical systems, where
the free energy of one sys
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