Temperature in Quantum Systems: Meaning & Impact

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What is the meaning of temperature in a quantum system? Surely temperature concerns lots of particles. (More is different. -Philip W. Anderson) So the wave function of the system is very very big. Could temperature only exist in a mixed state system. But how do we define temperature? How does temperature influence the evolution of the system? The Schrodinger equation alone controls the evolution of the system already.
 
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Quantum River said:
What is the meaning of temperature in a quantum system? Surely temperature concerns lots of particles. (More is different. -Philip W. Anderson) So the wave function of the system is very very big. Could temperature only exist in a mixed state system. But how do we define temperature? How does temperature influence the evolution of the system? The Schrodinger equation alone controls the evolution of the system already.

The formalism of QM doesn't account for a description of the physical quantity called "temperature". However, we can describe quantum mechanically a statistical system for which we know to define the temperature.
 
Quantum River said:
What is the meaning of temperature in a quantum system? Surely temperature concerns lots of particles. (More is different. -Philip W. Anderson) So the wave function of the system is very very big. Could temperature only exist in a mixed state system. But how do we define temperature? How does temperature influence the evolution of the system? The Schrodinger equation alone controls the evolution of the system already.

Visit also "Energy Vs Information" session
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!

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