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Thermodynamic Potentials01:26

Thermodynamic Potentials

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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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The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an...
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Maxwell-Boltzmann Distribution: Problem Solving01:20

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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The Collision Theory
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Thermodynamics: Chemical Potential and Activity01:10

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The effective concentration of a species in a solution can be expressed precisely in terms of its activity. Activity considers the effect of electrolytes present in the vicinity of the species of interest and depends on the ionic strength of the solution. The activity of a species is expressed as the product of molar concentration and the activity coefficient of the species.
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Temperature Dependent Deformation01:12

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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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Probing the partition function for temperature-dependent potentials with nested sampling.

Lune Maillard1, Philippe Depondt1, Fabio Finocchi1

  • 1Sorbonne Université, CNRS, Institut des Nanosciences de Paris, INSP, F-75005 Paris, France.

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|November 13, 2025
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Summary
This summary is machine-generated.

A new method using an extended partition function simplifies calculating thermodynamic properties. This approach efficiently computes the partition function, even with temperature-dependent energies, saving significant computational time.

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Area of Science:

  • Computational physics
  • Statistical mechanics
  • Physical chemistry

Background:

  • Thermodynamic properties are typically derived from the partition function.
  • Evaluating the partition function for many-atom systems is computationally challenging due to the summation over microscopic states.
  • Nested sampling, a Bayesian method, can compute the partition function and density of states efficiently, but struggles with temperature-dependent potentials.

Purpose of the Study:

  • To develop a novel method for efficiently computing partition functions with temperature-dependent potentials.
  • To overcome the computational limitations of standard nested sampling for temperature-dependent systems.
  • To restore the efficiency of nested sampling for calculating thermodynamic properties across various temperatures.

Main Methods:

  • Introduction and implementation of an extended partition function approach.
  • Treating temperature as an additional parameter to be sampled within nested sampling.
  • Applying the extended partition function method to compute quantum partition functions for harmonic potentials and Lennard-Jones clusters.

Main Results:

  • The extended partition function allows for nested sampling in a single run, irrespective of temperature dependence.
  • The new method significantly reduces computational time compared to performing nested sampling at each temperature.
  • Demonstrated superior performance for computing quantum partition functions for specific systems at low temperatures.

Conclusions:

  • The extended partition function method offers a computationally efficient solution for calculating thermodynamic properties.
  • This approach is particularly advantageous for systems with temperature-dependent effective potentials.
  • The method shows promise for broader applications in statistical mechanics and computational chemistry.