Entropy

Research

18 pages, 315 KiB

Open AccessArticle

Rethinking Economic Measurement Using Statistical Ensembles

by Cal Abel

Entropy 2025, 27(3), 265; https://doi.org/10.3390/e27030265 - 3 Mar 2025

Viewed by 988

The axiomatic framework of quantum game theory gives us a new platform for exploring economics by resolving the foundational problems that have long plagued the expected utility hypothesis. This platform gives us a previously unrecognized tool in economics, the statistical ensemble, which we [...] Read more.

The axiomatic framework of quantum game theory gives us a new platform for exploring economics by resolving the foundational problems that have long plagued the expected utility hypothesis. This platform gives us a previously unrecognized tool in economics, the statistical ensemble, which we apply across three distinct economic spheres. We examine choice under uncertainty and find that the Allais paradox disappears. For over seventy years, this paradox has acted as a barrier to investigating human choice by masking actual choice heuristics. We discover a powerful connection between the canonical ensemble and neoclassical economics and demonstrate this connection’s predictive capability by examining income distributions in the United States over 24 years. This model is an astonishingly accurate predictor of economic behavior, using just the income distribution and the total exergy input into the economy. Finally, we examine the ideas of equality of outcome versus equality of opportunity. We show how to formally consider equality of outcome as a Bose–Einstein condensate and how its achievement leads to a corresponding collapse in economic activity. We call this new platform ‘statistical economics’ due to its reliance on statistical ensembles. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

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12 pages, 614 KiB

Open AccessArticle

Three Optima of Thermoelectric Conversion: Insights from the Constant Property Model

by Paul Raux, Christophe Goupil and Gatien Verley

Entropy 2025, 27(3), 252; https://doi.org/10.3390/e27030252 - 27 Feb 2025

Viewed by 369

Abstract

Starting from Ioffe’s description of a thermoelectric converter, we recover the optimal working points of conversion: the point of maximum efficiency and the one of maximal power. Inspired by biological converters’ optimization, we compute a third optimal point associated with cost of energy [...] Read more.

Starting from Ioffe’s description of a thermoelectric converter, we recover the optimal working points of conversion: the point of maximum efficiency and the one of maximal power. Inspired by biological converters’ optimization, we compute a third optimal point associated with cost of energy (COE). This alternative cost function corresponds to the amount of heat exchanged with the cold reservoir per unit of electric current used. This work emphasizes the symmetry between the efficiency and performance coefficient of the electric generator and heat pump modes. It also reveals the relation between their optimal working points. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

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18 pages, 3516 KiB

Open AccessArticle

Temperature Gradients as a Data Storage Principle

by Jeroen Schoenmaker, Pâmella Gonçalves Martins and Julio Carlos Teixeira

Entropy 2025, 27(2), 129; https://doi.org/10.3390/e27020129 - 26 Jan 2025

Viewed by 1257

Abstract

In this work, we analyze the thermodynamic principles underlying modern data storage systems, including Random Access Memory (RAM), hard disk drive (HDD), flash memory, magnetic RAM (MRAM), ferroelectric RAM (FeRAM), and phase-change RAM (PCRAM), as well as other less well-known data storage mechanisms. [...] Read more.

In this work, we analyze the thermodynamic principles underlying modern data storage systems, including Random Access Memory (RAM), hard disk drive (HDD), flash memory, magnetic RAM (MRAM), ferroelectric RAM (FeRAM), and phase-change RAM (PCRAM), as well as other less well-known data storage mechanisms. The analysis is conducted in the context of data storage and processing in relation to Landauer’s principle, with special emphasis on hysteresis. Analogous to how heat engines are characterized by thermodynamic cycles, data storage systems are examined in terms of the hysteresis loop of their fundamental data unit. We explore the role of heat in data storage systems. Afterward, we introduce the concept of temperature gradient memory (TeGraM) along with a detailed layout of a realizable device. Experimental results demonstrating this technology are also presented. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

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6 pages, 181 KiB

Open AccessArticle

The Gibbs Fundamental Relation as a Tool for Relativity

by Friedrich Herrmann and Michael Pohlig

Entropy 2025, 27(1), 74; https://doi.org/10.3390/e27010074 - 15 Jan 2025

Viewed by 656

Abstract

When relativistic physics is lectured on, interest is focused on the behavior of mechanical and electromagnetic quantities during a reference frame change. However, not only mechanical and electromagnetic quantities transform during a reference frame change; thermodynamic and chemical quantities do too. We will [...] Read more.

When relativistic physics is lectured on, interest is focused on the behavior of mechanical and electromagnetic quantities during a reference frame change. However, not only mechanical and electromagnetic quantities transform during a reference frame change; thermodynamic and chemical quantities do too. We will study the transformations of temperature and chemical potential, show how to obtain the corresponding transformation equations with little effort, and exploit the fact that the energy conjugate extensive quantities, namely entropy and amount of substance, are Lorentz-invariant. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

12 pages, 261 KiB

Open AccessArticle

Fundamental Limits of an Irreversible Heat Engine

by Rui Fu

Entropy 2024, 26(12), 1128; https://doi.org/10.3390/e26121128 - 23 Dec 2024

Viewed by 713

Abstract

We investigated the optimal performance of an irreversible Stirling-like heat engine described by both overdamped and underdamped models within the framework of stochastic thermodynamics. By establishing a link between energy dissipation and Wasserstein distance, we derived the upper bound of maximal power that [...] Read more.

We investigated the optimal performance of an irreversible Stirling-like heat engine described by both overdamped and underdamped models within the framework of stochastic thermodynamics. By establishing a link between energy dissipation and Wasserstein distance, we derived the upper bound of maximal power that can be delivered over a complete engine cycle for both models. Additionally, we analytically developed an optimal control strategy to achieve this upper bound of maximal power and determined the efficiency at maximal power in the overdamped scenario. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

33 pages, 5394 KiB

Open AccessFeature PaperArticle

Carnot and the Archetype of Waterfalls

by Hans U. Fuchs, Elisabeth Dumont and Federico Corni

Entropy 2024, 26(12), 1066; https://doi.org/10.3390/e26121066 - 7 Dec 2024

Cited by 1 | Viewed by 942

Abstract

Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of [...] Read more.

Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of waterfalls to causative thermal processes: heat powers motion in a heat engine just as falling water does when activating rotation in a water wheel. We understand Carnot’s waterfall imagery as an archetype of human reasoning—as an embodiment of how we experience and understand causative (agentive) phenomena. We project it onto the macroscopic phenomena identified in physical science and so unlock the power of analogical structure mapping between theories of fluids, electricity and magnetism, heat, substances, gravity, and linear and rotational motion. In particular, the notion of (motive) power of a waterfall lets us create imaginative explanations of the interactions of Forces of Nature and helps us construct a generalized energy principle. Two-hundred years after Carnot made us aware of it, his Waterfall Analogy is a powerful example of theory construction with roots deep in how we experience phenomena as caused by natural agents. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

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21 pages, 478 KiB

Open AccessArticle

Exploring the Thermodynamic Uncertainty Constant: Insights from a Quasi-Ideal Nano-Gas Model

by Giorgio Sonnino

Entropy 2024, 26(12), 1011; https://doi.org/10.3390/e26121011 - 23 Nov 2024

Viewed by 665

Abstract

In previous work, we investigated thermodynamic processes in systems at the mesoscopic level where traditional thermodynamic descriptions (macroscopic or microscopic) may not be fully adequate. The key result is that entropy in such systems does not change continuously, as in macroscopic systems, but [...] Read more.

In previous work, we investigated thermodynamic processes in systems at the mesoscopic level where traditional thermodynamic descriptions (macroscopic or microscopic) may not be fully adequate. The key result is that entropy in such systems does not change continuously, as in macroscopic systems, but rather in discrete steps characterized by the quantization constant

β

. This quantization reflects the underlying discrete nature of the collision process in low-dimensional systems and the essential role played by thermodynamic fluctuations at this scale. Thermodynamic variables conjugate to the forces, along with Glansdorff–Prigogine’s dissipative variable can be discretized, enabling a mesoscopic-scale formulation of canonical commutation rules (CCRs). In this framework, measurements correspond to determining the eigenvalues of operators associated with key thermodynamic quantities. This work investigates the quantization parameter

β

in the CCRs using a nano-gas model analyzed through classical statistical physics. Our findings suggest that

β

is not an unknown fundamental constant. Instead, it emerges as the minimum achievable value derived from optimizing the uncertainty relation within the framework of our model. The expression for

β

is determined in terms of the ratio

χ

, which provides a dimensionless number that reflects the relative scales of volume and mass between entities at the Bohr (atomic level) and the molecular scales. This latter parameter quantifies the relative influence of quantum effects versus classical dynamics in a given scattering process. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

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19 pages, 903 KiB

Open AccessFeature PaperArticle

A Contemporary View on Carnot’s Réflexions

by Jan-Peter Meyn

Entropy 2024, 26(12), 1002; https://doi.org/10.3390/e26121002 - 21 Nov 2024

Viewed by 693

Abstract

Entropy and energy had not yet been introduced to physics by the time Carnot wrote his seminal Réflexions. Scholars continue to discuss what he really had in mind and what misconceptions he might have had. Actually, his work can be read as a [...] Read more.

Entropy and energy had not yet been introduced to physics by the time Carnot wrote his seminal Réflexions. Scholars continue to discuss what he really had in mind and what misconceptions he might have had. Actually, his work can be read as a correct introduction to the physics of heat engines when the term calorique is replaced by entropy and entropy is used as the other fundamental thermal quantity besides temperature. Carnot’s concepts of falling entropy as an analogy to the waterfall, and the separation of real thermal processes into reversible and irreversible processes are adopted. Some details of Carnot’s treatise are ignored, but the principal ideas are quoted and assumed without modification. With only two thermal quantities, temperature and entropy, modern heat engines can be explained in detail. Only after the principal function of heat engines is developed is energy introduced as physical quantity in order to compare thermal engines with mechanical and electrical engines and, specifically, to calculate efficiency. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

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18 pages, 413 KiB

Open AccessArticle

Phase Space Spin-Entropy

by Davi Geiger

Entropy 2024, 26(5), 372; https://doi.org/10.3390/e26050372 - 28 Apr 2024

Viewed by 2441

Abstract

Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a state. The degrees of freedom of a [...] Read more.

Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a state. The degrees of freedom of a quantum state are position and spin. We focus on the spin degree of freedom and elucidate the spin-entropy. Then, we present some of its properties and show how entanglement increases spin-entropy. A dynamic model for the time evolution of spin-entropy concludes the paper. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

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21 pages, 392 KiB

Open AccessArticle

Testing the Minimum System Entropy and the Quantum of Entropy

by Uwe Hohm and Christoph Schiller

Entropy 2023, 25(11), 1511; https://doi.org/10.3390/e25111511 - 3 Nov 2023

Cited by 1 | Viewed by 3119

Abstract

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy

S ⩾ k ln 2

. We clarify in which cases it is possible to speak about a minimum system entropy [...] Read more.

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy

S ⩾ k ln 2

. We clarify in which cases it is possible to speak about a minimum system entropy

k ln 2

and in which cases about a quantum of entropy. Conceptual tensions with the third law of thermodynamics, with the additivity of entropy, with statistical calculations, and with entropy production are resolved. Black hole entropy is surveyed. Claims for smaller system entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time here, also implies the minimum system entropy

k ln 2

. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of minimum system entropy enable one to speak about a general principle that is valid across nature. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

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200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824

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