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Entropy02:39

Entropy

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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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.
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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
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Quadratic Equations in the Complex Number System01:29

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A quadratic equation in the form ax2+bx+c=0 can have solutions that vary in nature depending on the value of the discriminant, b2−4ac. In this expression, a is the coefficient of the quadratic term x2, b is the coefficient of the linear term x, and c is the constant term. When the discriminant is negative, the equation has no real number solutions. However, by introducing complex numbers through the imaginary unit i, defined by i=-1, these equations can still be solved.The square root of...
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Chemical Equations03:10

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Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of the equation. The substances generated by the reaction are called products, and their formulas are placed on the right side of the equation. Plus signs (+) separate individual reactant and product formulas, and an arrow (→) separates the reactant and product (left and right)...
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Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.
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The MultiBac Protein Complex Production Platform at the EMBL
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Entropy production for complex Langevin equations.

Simone Borlenghi1, Stefano Iubini2,3, Stefano Lepri3,4

  • 1Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden.

Physical Review. E
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Summary
This summary is machine-generated.

This study explores irreversible processes in nonlinear oscillator networks using complex-valued Langevin equations. Researchers quantified entropy production rates in nonequilibrium steady states, highlighting the impact of asymmetric coupling.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Nonlinear oscillators coupled to thermochemical baths exhibit complex behaviors.
  • Understanding irreversible processes and entropy production is crucial in nonequilibrium systems.
  • Non-Hermitian Hamiltonians are used to model dissipation in quantum and classical systems.

Purpose of the Study:

  • To investigate irreversible processes in nonlinear oscillator networks.
  • To compute entropy production rates using stochastic thermodynamics.
  • To analyze nonequilibrium steady states and the role of asymmetric coupling.

Main Methods:

  • Modeling nonlinear oscillators with complex-valued Langevin equations.
  • Introducing dissipation through non-Hermitian terms in the Hamiltonian.
  • Applying stochastic thermodynamics formalism to derive entropy production rates.

Main Results:

  • Explicit expressions for entropy production rates were derived.
  • Nonequilibrium steady states were characterized by constant entropy production and steady currents.
  • Numerical calculations for a 1D chain and a dimer demonstrated the effect of asymmetric coupling on entropy production.

Conclusions:

  • The study provides a framework for analyzing irreversible processes in complex oscillator networks.
  • Asymmetric coupling significantly influences entropy production in these systems.
  • The findings contribute to the understanding of nonequilibrium statistical mechanics and complex systems.