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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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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
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The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...
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Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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Apparent Pathologies in Stochastic Entropy Production in the Thermalisation of an Open Two-Level Quantum System.

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Area of Science:

  • Quantum thermodynamics
  • Statistical mechanics
  • Open quantum systems

Background:

  • Investigating the entropic consequences of open quantum system relaxation.
  • Utilizing quantum state diffusion framework for evolution dynamics.

Purpose of the Study:

  • To demonstrate thermalization is accompanied by persistent non-zero mean rate of change of stochastic entropy production.
  • To associate this thermodynamic signature with the purification of the reduced density matrix.
  • To address mathematical difficulties in computing stochastic entropy production.

Main Methods:

  • Quantum state diffusion framework.
  • Minimal set of raising and lowering Lindblad operators.
  • Analysis of reduced density matrix purification versus ensemble average impurity.

Main Results:

  • Thermalization typically shows persistent non-zero mean rate of stochastic entropy production.
  • This signature is linked to reduced density matrix purification.
  • Stationary statistics with zero entropy production achieved after purity.
  • Mathematical difficulties in entropy production computation resolved by coordinate choice.

Conclusions:

  • Frameworks for modeling open systems require careful selection for thermodynamic and dynamic behavior.
  • Purification of the reduced density matrix is a key indicator during thermalization.
  • Understanding stochastic entropy production is crucial for open quantum system dynamics.