Finite-Time Thermodynamics in Economics
Abstract
:1. Introduction
2. Major Types of Economic Agents and Their Characteristics
- Economic agents whose resource estimates depend on the agent’s state (on its stocks of resources and capital). Usually, but not always, when the stock of a resource is decreasing its estimate is decreasing too, and when capital is increasing then the estimate is increasing. The economic agent can also exchange capital with the environment. Here, the minimal price of selling (maximal price of buying) is the economic agent’s estimate of capital. We denote it as . We shall call such systems economic systems with finite capacity.
- Economic agents with estimates independent of stocks of the resource are similar to thermodynamic systems with infinite capacity (reservoirs). We shall call them economic reservoirs. Economic markets where prices do not depend on the rate of trading are examples of economic reservoirs. The amount of resource that is sold/purchased here is so small in comparison with its stock that in practice it does not effect its estimate.In the general case, a market’s demand/supply function depends on the prices of selling (buying) and on the estimates, and it obeys the conditions (1) for resource exchange kinetics. Such a market is called monopolistic. In the limit when for each flow the difference between the price and estimate is infinitesimal (prices for any rate of flow are equal to the market estimates), then the market is called a market with perfect competition. If this market is a reservoir then its prices do not depend on the demand but change over time under the influence of the external system factors.
- Intermediaries (firms) are active economic agents which set the price or rate of resource selling (buying) independently of its stock in such a way that they extract maximum amount of capital. They are similar to a heat engine working fluid in thermodynamics. They can contact with a number of economic agents simultaneously setting different prices and flows for each of them. The intermediary’s prices and its function that describes when to establish/break contact with an economic agent are controls.A firm can be a manufacturing firm which buys resources (raw materials, labor, or equipment) and sells its production, which is determined by its production function [1] and the price it sets. We denote the price for the -th resource set by a firm as .
2.1. Wealth Function and Capital Dissipation
2.2. Differential Links between Estimates—Economic Analogue of the Gibbs–Duhem Relation
2.3. Capital Dissipation
2.4. The Second Law of Microeconomics
3. Economic Balances and Capital Dissipation
3.1. Open Systems
3.2. Isolated Systems
3.3. Maximum Profit Flow
4. Resource Exchange in Isolated Systems
Resource/Capital Exchange in Economic Systems with Different Configurations
5. Stationary State of an Open Economic System
6. Principle of Minimal Capital Dissipation
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Thermodynamic System | Economic System | ||
---|---|---|---|
Name | Notation | Name | Notation |
Temperature of a system with finite capacity | The reciprocal of capital estimate for EA | ||
Reservoir (irreversible heat exchange) | Monopolistic market | ||
Mass | Resource stock | ||
Finite-capacity system, chemical potential | Economic agent, resource estimate | ||
Temperature of the working fluid for heat engine | Intermediary, price | ||
Free energy | Capital | ||
Internal energy | Capitalization | ||
Entropy | Wealth function | ||
Entropy production | Capital dissipation |
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Tsirlin, A.; Gagarina, L. Finite-Time Thermodynamics in Economics. Entropy 2020, 22, 891. https://doi.org/10.3390/e22080891
Tsirlin A, Gagarina L. Finite-Time Thermodynamics in Economics. Entropy. 2020; 22(8):891. https://doi.org/10.3390/e22080891
Chicago/Turabian StyleTsirlin, Anatoly, and Larisa Gagarina. 2020. "Finite-Time Thermodynamics in Economics" Entropy 22, no. 8: 891. https://doi.org/10.3390/e22080891
APA StyleTsirlin, A., & Gagarina, L. (2020). Finite-Time Thermodynamics in Economics. Entropy, 22(8), 891. https://doi.org/10.3390/e22080891