Determination of Nonequilibrium Temperature and Pressure using Clausius Equality in a State with Memory: A Simple Model Calculation
Abstract
Use of the extended definition of heat dQ=deQ+diQ converts the Clausius inequality dS greater than or equal to deQ/T0 into an equality dS=dQ/T involving the nonequilibrium temperature T of the system having the conventional interpretation that heat flows from hot to cold. The equality is applied to the exact quantum evolution of a 1-dimensional ideal gas free expansion. In a first ever calculation of its kind in an expansion which retains the memory of initial state, we determine the nonequilibrium temperature T and pressure P, which are then compared with the ratio P/T obtained by an independent method to show the consistency of the nonequilibrium formulation. We find that the quantum evolution by itself cannot eliminate the memory effect.cannot eliminate the memory effect; hence, it cannot thermalize the system.
Keywords
Cite
@article{arxiv.1512.08744,
title = {Determination of Nonequilibrium Temperature and Pressure using Clausius Equality in a State with Memory: A Simple Model Calculation},
author = {P. D. Gujrati},
journal= {arXiv preprint arXiv:1512.08744},
year = {2016}
}
Comments
5 pages, 4 figures; the new version contains some new references and the new result that the definition of temperature, pressure, etc. satisfies the second law. The text is also rewritten at some places