From Phase Space to Non-Equilibrium Dynamics: Exploring Liouville’s Theorem and Its Implications
Source abstract
Abstract
We generalize Liouville’s theorem to incorporate entropy gradients in phase space, demonstrating that non-equilibrium systems exhibit compressible phase-space dynamics (dρ/dt≠0). This framework bridges Hamiltonian mechanics and thermodynamics, with applications in beam stacking, stochastic cooling, and quantum thermalization. Numerical simulations validate the theory, showing entropy stabilization at S≈1.382 (error <5×10−5) for N=104 particles.
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Research context
OpenAlex topics: Quantum Mechanics and Applications · Advanced Thermodynamics and Statistical Mechanics · Quantum chaos and dynamical systems
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Affiliations
Department of Physics, Instituto Superior Técnico—IST, Universidade de Lisboa—UL, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
References (53)
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