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Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

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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.
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One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
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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 spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
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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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The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...
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Neural Thermodynamic Integration: Free Energies from Energy-Based Diffusion Models.

Bálint Máté1,2,3, François Fleuret2, Tristan Bereau1

  • 1Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg, Germany.

The Journal of Physical Chemistry Letters
|November 6, 2024
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Summary
This summary is machine-generated.

Neural TI uses a neural network to perform thermodynamic integration (TI) for free-energy calculations. This approach accurately computes excess chemical potential in Lennard-Jones fluids from a single simulation, reducing computational cost.

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Area of Science:

  • Computational chemistry
  • Statistical mechanics
  • Machine learning

Background:

  • Thermodynamic integration (TI) is a rigorous method for free-energy calculations.
  • TI is computationally expensive and requires sampling many intermediate ensembles.
  • Current TI methods are limited in the degrees of freedom they can handle.

Purpose of the Study:

  • To develop a more efficient method for thermodynamic integration.
  • To reduce the computational cost of free-energy calculations.
  • To enable TI for systems with many degrees of freedom.

Main Methods:

  • Proposed Neural TI, a method using a trainable neural network for TI.
  • Parametrized a time-dependent Hamiltonian interpolating between systems.
  • Optimized the Hamiltonian's gradient using a score matching objective.
  • Utilized an energy-based diffusion model to sample intermediate ensembles.

Main Results:

  • Neural TI accurately calculates excess chemical potential for Lennard-Jones fluids.
  • The method performs TI from a single reference calculation.
  • Achieved accurate free-energy changes without simulating intermediate Hamiltonians.

Conclusions:

  • Neural TI offers a computationally efficient alternative to traditional TI.
  • The method demonstrates the potential of machine learning in free-energy calculations.
  • Neural TI can overcome limitations of current TI methods in terms of computational cost and system complexity.