Generalization of the second law for a nonequilibrium initial state |
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Authors: | H-H Hasegawa J Ishikawa DJ Driebe |
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Institution: | a Department of Mathematical Sciences, Ibaraki University, Bunkyo, Mito 310-8512, Japan b Division of Math, Science and Technology, Nova Southeastern University, Fort Lauderdale, FL 33314, USA |
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Abstract: | We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function but also tells us the maximum work that may be gained from a nonequilibrium initial state. The generalized second law also gives a fundamental relation between work and information. It is valid even for a small Hamiltonian system not in contact with a heat reservoir but with an effective temperature determined by the isentropic condition. Our relation can be tested in the Szilard engine, which will be realized in the laboratory. |
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