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The Second Law of Thermodynamics

The Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...

Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...

Second Law of Thermodynamics

Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

Second Law of Thermodynamics

Second Law of Thermodynamics

The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...

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Related Experiment Video

Updated: Nov 27, 2025

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

A Survey on Entropy and Economic Behaviour.

Ziv Hellman¹, Ron Peretz¹

¹Department of Economics, Bar-Ilan University, 5290002 Ramat Gan, Israel.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

Entropy significantly impacts game theory and economic behavior, revealing strong links between memory and entropy in repeated games. It also measures information value in noisy signals, informing rational inattention theories.

Keywords:

bounded memory bounded rationality entropy method repeated games

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Area of Science:

Game Theory
Information Theory
Behavioral Economics

Background:

Entropy is crucial in understanding decision-making and economic behavior.
Bounded recall capacity in players affects outcomes in interactive games.
Classic experiment ordering is a partial order, motivating extensions.

Purpose of the Study:

To survey results on games with bounded recall, highlighting memory-entropy relations.
To explore entropy's use in valuing information from noisy signals.
To connect these concepts to rational inattention theory.

Main Methods:

Analysis of repeated games with players having bounded recall.
Representation of noisy signals as stochastic matrices.
Extension of Blackwell's experiment ordering using entropy differences.

Main Results:

Strong relationships found between memory and entropy in bounded recall games.
Entropy difference serves as a proposed extension to Blackwell's experiment ordering.
Modeling attention limits as Shannon channel capacity explains economic phenomena.

Conclusions:

Entropy provides key insights into strategic complexity and information value.
Bounded recall and entropy are intrinsically linked in game theory.
The rational inattention framework, using information theory, explains observed economic behaviors.