2009/07/09 by H. -H. Hasegawa, Hiroshi Hasegawa, Junichi Ishikawa +4 · 99 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boltzmann constant #Classical mechanics #Distribution function #Entropy (arrow of time) #Function (biology) #Isentropic process #Isothermal process #Mathematics #Non-equilibrium thermodynamics #Physics #Second law of thermodynamics #State function #Statistical Mechanics and Entropy #Statistical physics #Thermodynamics #Work (physics) #cond-mat.stat-mech #thermodynamics and calorimetric analyses
paper · pdf · doi:10.1016/j.physleta.2009.12.042
published in Physics Letters A 374(8), 1001-1004 (Elsevier BV)
arxiv created 2009/07/09 · openalex publication_date 2009/12/19 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.