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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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Maxwell's Thermodynamic Relations01:23

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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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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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Third Law of Thermodynamics02:38

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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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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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Thermodynamics: Activity Coefficient01:24

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Activity is the measure of the effective concentration of the species in solution. It can be expressed as the product of the molar concentration of the species and its activity coefficient. The activity coefficient is a dimensionless quantity and depends on the total ionic strength of the solution.
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Thermodynamic Bounds on Correlation Times.

Andreas Dechant1, Jérôme Garnier-Brun2,3, Shin-Ichi Sasa1

  • 1Department of Physics #1, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.

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This summary is machine-generated.

We found new speed limits for how quickly physical properties self-average in diffusive systems. These limits reveal how steady-state entropy production accelerates self-averaging out of equilibrium.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Physical Chemistry

Background:

  • Physical observables in diffusive systems exhibit correlation times that govern their self-averaging properties.
  • Understanding these correlation times is crucial for characterizing system dynamics, both in and out of equilibrium.

Purpose of the Study:

  • To derive a variational expression for the correlation time in steady-state diffusive systems.
  • To establish lower bounds on correlation time, defining speed limits for observable self-averaging.
  • To investigate how these speed limits behave out of equilibrium and their relation to entropy production.

Main Methods:

  • Derivation of a variational expression for correlation time.
  • Establishing lower bounds on correlation time in equilibrium and non-equilibrium steady states.
  • Relating non-equilibrium speed limits to entropy production rate and geometric structure of irreversible currents.

Main Results:

  • A variational expression for correlation time is derived, yielding lower bounds that act as speed limits for self-averaging.
  • In equilibrium, a trade-off between long- and short-time fluctuations defines the bound.
  • Out of equilibrium, this trade-off can be violated, accelerating self-averaging and linked to entropy production.

Conclusions:

  • The derived speed limits provide fundamental constraints on the rate of self-averaging in diffusive systems.
  • Violation of the equilibrium trade-off out of equilibrium is directly related to the system's dissipation rate.
  • These findings offer a method to estimate entropy production from time-symmetric observables, even in the absence of observable time-reversal symmetry breaking.