The following “As is …”;
This statistical–mechanical model is based on the Boltzmann–Lotka–Volterra ( BLV ) method.
BLV models involve two components: a fast equilibration, Boltzmann, component and a slow dynamic, Lotka–Volterra, component. The Boltzmann component applies maximum entropy principle to derive the static flow patterns of instruments (or their utility, as is the case). The Lotka–Volterra component evolves the spatial distribution (Price & Time; i.e.the chart) and the flow pattern of a information according to generalized Lotka–Volterra equations for distributed information.
The resultant dynamics exhibit critical regimes, interpreted as phase transitions, where a small variation in suitably chosen (control) parameters changes the global outcomes measured via specific aggregated quantities (order parameters).
The main take-away here is that this is in line with the idea that, despite the complexity of such a system (as depicted) only few parameters may be necessary to understand drastic macroscopic changes.
The maximum entropy method has been applied to a variety of collective phenomena (E.g., Speculation; Yours Truly) suggesting a formal analogy between complex, socio-economic systems and thermodynamic systems.
We use a clear thermodynamic interpretation of the Fisher information as the second derivative of free entropy. Specifically, we investigate the minimum work required to vary a control parameter and trace configuration entropy and internal energy, according with the first law of thermodynamics. The thermodynamic work is defined via Fisher information and thus can be computed solely based on probability distributions estimated from available data.
Once we introduce the concept of thermodynamic efficiency as the ratio of the order gained during a change to the required work (information transmission), it can be rather easily demonstrated that it is maximized at criticality.
Note; The above further illustrates the common observation that Technical Analysis fails, in most cases, to capture (forecast) Finite-time Singularities – i.e the sudden appearance of exponential price increases or price collapses (crashes).
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