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A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
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Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...
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Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:
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Thermodynamic Potentials01:26

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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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Statements of the Second Law of Thermodynamics01:15

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The second law of thermodynamics can be stated in several different ways, and all of them can be shown to imply the others. The Clausius’ statement of the second law of thermodynamics is based on the irreversibility of spontaneous heat flow. It states that heat will not flow from the colder body to the hotter body unless some other process is involved. Additionally, as per the Kelvin’s statement, it is impossible to convert the heat from a single source into work without any other...
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Zeroth Law of Thermodynamics01:14

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Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. That statement of transitivity is called the "zeroth law of thermodynamics." For example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually, the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium.
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Updated: Jun 20, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Semiclassical thermodynamic geometry.

L F Escamilla-Herrera1, J L López-Picón1, José Torres-Arenas1

  • 1División de Ciencias e Ingenierías Campus León, Universidad de Guanajuato, AP E-143, CP 37150, León, Guanajuato, México.

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Summary

This study analyzes thermodynamic geometry (TG) in semiclassical fluids. Quantum effects in hard-sphere models avoid anomalies seen in classical systems, and square-well models show unique curvature behaviors with changing quantum contributions.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Quantum Fluids

Background:

  • Thermodynamic geometry (TG) provides insights into fluid behavior.
  • Classical hard-sphere fluids exhibit anomalies in TG related to scalar curvature sign.
  • Understanding semiclassical fluid behavior requires incorporating quantum effects.

Purpose of the Study:

  • To analyze the thermodynamic geometry of semiclassical fluids.
  • To investigate how quantum contributions affect TG anomalies.
  • To explore the behavior of semiclassical square-well fluids and their curvature properties.

Main Methods:

  • Path-integral Monte Carlo simulations to determine Helmholtz free energy for semiclassical hard-sphere (SCHS) fluids.
  • Analysis of scalar curvature in semiclassical fluids.
  • Comparison of semiclassical and classical fluid behaviors across different thermodynamic conditions.

Main Results:

  • Quantum contributions in SCHS fluids avoid TG anomalies observed in classical hard-sphere systems over a significant thermodynamic range.
  • The semiclassical curvature scalar's behavior was analyzed concerning the thermal de Broglie wavelength for square-well fluids.
  • Semiclassical R Widom lines were described and compared to classical systems.

Conclusions:

  • Quantum effects significantly alter the thermodynamic geometry of fluids, mitigating classical anomalies.
  • Semiclassical models offer a richer understanding of fluid behavior, particularly in systems with attractive interactions.
  • The study provides a framework for analyzing quantum fluid properties using thermodynamic geometry.