Ergodit

An ergodic equation: 

where

${\displaystyle V_{T}\,}$ is the velocity of money for all transactions in a given time frame;

${\displaystyle P\,}$ is the price level;

${\displaystyle T\,}$ is the aggregate real value of transactions in a given time frame; and

${\displaystyle M\,}$ is the total nominal amount of money in circulation on average in the economy (see “Money supply” for details).

We try to remain ergodic, but it is an adaptive process.   The average of the total aggregate money times rate of transactions over a time interval  should be equal to the sum of all goods goods..

The banks and value chains to maintain ergodicity. by keeping congestion in flows bound.  Being a self sampled system, they can only do that to some limited precision.  

Rate of turn over times money = average price per good times total transactions

It is ergodic with respect to Vt, the turn over rate.   

Ergodic means no superposition of partitions, it implies we can sum over any partial sequence but when their are partitions that do not mix, we have so superimpose the sum over partitions, it is not ergodic. The definition is related to the Shannon-Nyquist for 2D systems.

Notice atomic orbitals, any integration has to meet the boundary conditions.  That is not ergodic.  The exception are the low energy states which are not partitioned. But we assume ergodic in gas equations because the gas molecules are assumed prefect spheres.

In sanboc S/L pit, the pit boss bit error account measures deviation from ergodicity. Central banks collect fed taxes to attempt a force of ergodicity. Insurance companies care, they have to insure time. Season adjustment attempts to force ergodicity.  The betters solution is to keep a partitioned portfolio and superimpose.   In the3USA the election periods are design to both encourage and disrupt ergodicity. Ergodicity is an unnecessary cost.