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Related Concept Videos

Thermodynamics: Activity Coefficient01:24

Thermodynamics: Activity Coefficient

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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.
The activity coefficient is a measure of the deviation from ideal behavior. When the ionic strength of the solution is minimal, the activity coefficient of an ionic species is close to unity, making...
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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

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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Entropy01:18

Entropy

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
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Third Law of Thermodynamics02:38

Third Law of Thermodynamics

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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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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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Thermodynamic Correlation Inequality.

Yoshihiko Hasegawa1

  • 1Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

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Summary
This summary is machine-generated.

This study introduces a thermodynamic correlation inequality for Markov processes. It bounds the correlation function

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Area of Science:

  • Thermodynamics
  • Statistical Physics
  • Physical Systems Analysis

Background:

  • Fundamental limits on physical system operations are governed by trade-off relations.
  • Correlation functions quantify relationships between a system's present and future states.
  • Markov processes are a key model in statistical physics for describing systems evolving randomly over time.

Purpose of the Study:

  • To establish a novel trade-off relation for bounding the correlation function in Markov processes.
  • To introduce the concept of 'dynamical activity' as a thermodynamic measure.
  • To explore the implications of this trade-off for linear response theory.

Main Methods:

  • Derivation of a new trade-off relation, termed the thermodynamic correlation inequality.
  • Analysis of correlation functions within the framework of Markov processes.
  • Application of the derived inequality to linear response functions.

Main Results:

  • The change in the correlation function is bounded from above by dynamical activity.
  • Dynamical activity serves as a thermodynamic measure quantifying the overall activity of a Markov process.
  • The effect of perturbations on a system can be upper-bounded by its dynamical activity.

Conclusions:

  • The thermodynamic correlation inequality provides a fundamental bound on system dynamics.
  • Dynamical activity is identified as a crucial quantity limiting system correlations and response.
  • This work offers new insights into the interplay between thermodynamics, information, and system dynamics.