A Comprehensive Study of Statistical Mechanics in Financial Thermodynamic Systems

Abstract

Prokarsha Kumar Ghosh*

The stock market has been viewed as a dynamical system composed of complex interactions among top 100 firms of different stock indices as a time evolving network. This network has been constructed by stock price movements through regression analysis, capturing the changing structure of the market over time. A novel quantum statistical approach has been applied, where the network is treated as a system of energy states occupied by indistinguishable particles as bosons governed by Bose-Einstein statistics. In this paper partition functions have been used to define a thermodynamic entropy, which has been applied to identify structural changes during major financial events. Significant variations in entropy have been interpreted as indicators of systemic transitions in the market. The fitted temperature like parameter has been found to correlate with levels of economic development. Furthermore, financial systems have been conceptualized as condensates similar to Bose-Einstein condensates, and resulting statistical distributions have matched empirical patterns. Investment distributions have aligned with Pareto laws, and price movement distributions have resembled exponentially truncated distributions. These analogies and the integration of network modelling with quantum statistics, a thermodynamic framework has been established to capture complex market behaviours and systemic movements.

HTML PDF