Bookkeeping described as physical momentum.

Statistical Mechanics of a Time-Homogeneous System of Money and Antimoney
(Andreas Schacker, Matthias Schmitt, and Dieter Braun, Manuscript for PRE, 2012)
Financial crises appear throughout human history. Their interplay with the real economy has
puzzled generations of economists and is the subject of ongoing research. There are many schools
of thought on as to what are the actual causes of such crises and how monetary policy can try to
avert them. In particular, it has been suggested that the creation of credit money might be a source
of financial instability.
We explain how the credit mechanism in a system of fractional reserve banking leads to non-local
transfers of purchasing power which also affect non-involved agents. In an attempt to overcome this
issue and motivated by an analogy to physics, we impose the local symmetry of time homogeneity
on the monetary system. The resulting full reserve banking system suppresses non-local transfers
upon credit creation but has often been accused of stalling bank lending.
Starting from this premise, we consider a bi-currency system of non-bank assets (’money’) and
bank assets (’antimoney’) in which a payment can either be made by passing on money or by
receiving antimoney. As a result, a free floating exchange rate between non-bank assets and bank
assets is established. Interestingly, credit creation is then replaced by the simultaneous transfer
of money and antimoney at a negotiated exchange rate. By introducing this novel mechanism
of liquidity transfer, the issue of credit crunches commonly associated with full reserve banking
systems might be mitigated. Tools from statistical physics promise to provide new insight into
monetary and creditary dynamics.

Monetary Noether Theorem eliminates non-locality in monetary exchange
(Matthias Schmitt and Dieter Braun, Manuscript for PRL, 2011)
Money is conserved only if the monetary system is homogeneous in time. Violation of
this Noether relation leads to non-local interactions between money holders. Money
is represented as a particle-antiparticle pair of assets and liabilities. Value conser-
vation holds because transfers are invariant under exchange of trading roles. Money
conservation however is systematically violated if monetary pair creation by credit
is allowed. Normalization yields a fully symmetric monetary space: local, parallel
transfers of assets and liabilities replace non-local, time-asymmetric credit operations.
A liquidity market substitutes the credit market.

Bookkeeping Mistakes (PDF)
(Talk at the Monetary Reform Conference of the American Monetary Institute 2007)
Movie of the Talk:
Introduction (5 MB)
I: The hidden Currency of Banking (55 MB)
II: Towards Time Symmetric Money (21 MB)
III: Inflation from Random Transfer (11 MB)
IV: Wealth Concentration 16 MB)
Conclusion (7 MB)

Noether Theorem on Monetary Systems   (PDF without the movies)
(Talk at the spring meeting of the German Physical Society, 2007)
Abstract: Contrary to common belief, monetary systems can be implemented by bookkeeping in various ways.
I classify the implementations by the symmetry properties of their transactions. Each symmetry relates to a
conservation law in close analog to the Noether theorem:
- Symmetry of time asks for constant quantity of money
- Symmetry between transaction partners asks for zero profit
- Inclusion of the money issuer asks for internal exchange rates
Above relations can be directly visualized with a Feynman-Graph mapping of bookkeeping to mechanics.
I give real world examples on how above symmetries are not implemented by modern monetary systems.
Obeying the symmetries would implement monetary systems more stably with less inertial feedback loops.

The missing exchange rate of Banking,
Strong wealth condensation in stochastic transfer potential economies
(Posters at the spring meeting of the German Physical Society, 2006)

Nonequilibrium Thermodynamics of Wealth Condensation, Physica A, 369:714-722 (2006)
We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog
of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers
modes of wealth: random transfer, profit proportional to wealth and motivation of poor agents to work harder.
The economies never reach steady state. Wealth condensation is the result of stochastic tunneling through a metastable
transfer potential. In accordance with reality, both wealth and income distribution transiently show Pareto tails for high
income subjects. For metastable transfer potentials, exponential wealth condensation is a robust feature. For example
with 10 % annual profit 1% of the population owns 50 % of the wealth after 50 years. The time to reach such a strong
wealth condensation is a hyperbolic function of the annual profit rate.

Social Networks of Money analyzed with Feynman-Graphs (2005)
Talk given at the Frühjahrstagung of the German Physical Society