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Any Closed Thermodynamic System

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lamis
10 diapositives · 255 Views · Jul 15, 2014

This work explores the concept of Maxwell's Demon within the framework of thermodynamics and computation. It analyzes how a demon, when coupled with a thermal system, can effectively manipulate equilibrium states toward intermediate states. The findings suggest that, under certain conditions, this process can transpire without violating the second law of thermodynamics. Emphasizing Hamiltonian time evolution and phase-space conservation, this study delves into the implications of phase volumes and the nature of thermodynamic systems. The insights contribute to a better understanding of entropy and informational dynamics in thermodynamics.

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Any Closed Thermodynamic System
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  1. A Phase-Volume Based Exorcism of Maxwell’s DemonJohn D. NortonDepartment of History and Philosophy of ScienceUniversity of PittsburghBased on “All Shook Up: Fluctuations, Maxwell’s Demon and the Thermodynamics of Computation,” Section 4.www.pitt.edu/~jdnorton

  2. Any Closed Thermodynamic System

  3. Its Phase Space total phase volume V equilibrium states small fraction a of total volume intermediate states

  4. Assumption (a) • A Maxwell’s demon is a device that, • when coupled with a thermal system in • its final equilibrium state, • will, over time, assuredly or very likely lead the system to evolve to one of the intermediate states; • and, when its operation is complete, the thermal system remains in the intermediate state. Succeeds with all but small fraction b of equilibrium systems.

  5. Assumptions (b), (c) (b) The device returns to its initial state at the completion of the process; and it operates successfully for every microstate in that initial state. (c) The device and thermal system do not interact with any other systems.

  6. Assumption (a) V b demon degrees of freedom equilibrium states demon phase space volume v in initial = final state intermediate states a

  7. Assumptions (d), (e) and (f) (d) The time evolution of the total system is Hamiltonian with a time-reversible, time-independent Hamiltonian. (e) The final equilibrium state occupies all but a tiny portion α of the thermal system’s phase space, V, where α is very close to zero. (f) The intermediate states are all within the small remaining volume of phase space, αV.

  8. Contradiction Hamiltonian evolution of system + demon evolves much smaller phase volume vaV phase volume v(1-a)(1-b)V Liouville theorem Phase volume is conserved under Hamiltonian time development.

  9. Nota Bene (i) The second law of thermodynamics is not assumed to hold, so that the circularity troubling the information theoretic exorcisms does not arise (ii) The volumes of phase space representing states are not coarse grained; they consist simply of all those microstates upon which the demon can successfully act and the states that result. (iii) Thermodynamic entropy is not included in the argumentation.