A note on thermodynamics of the production processes

TL;DR

This paper models production as an open thermodynamic system, introducing a new factor called substitutive work and deriving production functions that clarify growth and factor contributions.

Contribution

It develops a thermodynamic-based heuristic model of production, incorporating substitutive work and technological characteristics to enhance analysis of production processes.

Findings

Thermodynamic principles help decompose output growth into technological and factor contributions.

Introduction of substitutive work as a production factor expands analysis capabilities.

The model provides a foundation for understanding labor-capital substitution in thermodynamic terms.

Abstract

The process of creating goods and services, measured by their value, is considered a process of creating complexity. This allows us to consider the production system as an open thermodynamic system, and to develop a simple heuristic model of the production process. The model includes three production factors: the index of complexity of production equipment (physical capital $K$), human activity (labour $L$), and the substitutive capacity of equipment (substitutive work $P$). The latter is a contribution to the theory of production from the thermodynamic approach, which also involves introducing technological characteristics of production equipment, such as labour requirement ($\overline{\lambda}$) and energy requirement ($\overline{\varepsilon}$), which indicate the amounts of labour and energy required to operate production equipment. By applying thermodynamic principles, we can understand how labour can be replaced by capital and derive the production function with four different formulations. Two of them are known and used by researchers for interpretation the production phenomena; the thermodynamic approach provides some foundation for economic theory, allowing us to decompose unambiguously the growth rate of output over technological level and the growth rates of production factors. Introducing substitute work as a factor of production and technological characteristics of capital expands our ability to plan and analyse production processes.