- Access by Xinjiang University
Nonequilibrium entropic temperature and its lower bound for quantum stochastic processes
Phys. Rev. E 89, 032148 – Published 31 March, 2014
DOI: https://doi.org/10.1103/PhysRevE.89.032148
Abstract
In this paper, we have studied the Shannon “entropic” nonequilibrium temperature (NET) of quantum Brownian systems. The Brownian particle is attached to either a bosonic or fermionic bath. Based on the Fokker-Planck description of the -number quantum Langevin equation, we have calculated entropy production, NET, and their bounds. Entropy production (EP), the upper bound of entropy production (UBEP), and the deviation of the UBEP from EP monotonically decrease as functions of time to equilibrium value for both of the thermal baths. The deviation decreases with increase of temperature of the bosonic thermal bath, but it becomes larger as the temperature of the fermionic bath grows. We also observe that nonequilibrium temperature and its lower bound monotonically increase to equilibrium value with the progression of time. But their difference as a function of time shows an optimum behavior in most cases. Finally, we have observed that at long time, the entropic temperature (for a bosonic thermal bath) first increases nonlinearly as a function of thermodynamic temperature (TT) and, if the TT is appreciably large, then it grows linearly. But for the fermionic thermal bath, the entropic temperature decreases monotonically as a nonlinear function of thermodynamic temperature to zero value.
Article Text
References (25)
- J. Casas-Vazquez and D. Jou, Rep. Prog. Phys. 66, 1937 (2003).
- T. Hatano and D. Jou, Phys. Rev. E 67, 026121 (2003).
- E. Bertin, K. Martens, O. Dauchot, and M. Droz, Phys. Rev. E 75, 031120 (2007).
- J. L. Garden, J. Richard, and H. Guillou, J. Chem. Phys. 129, 044508 (2008).
- W. G. Hoover and C. G. Hoover, Phys. Rev. E 77, 041104 (2008).
- A. Criado-Sancho, D. Jou, and J. Casas-Vazquez, Phys. Lett. A 372, 2172 (2008).
- K. R. Narayanan and A. R. Srinivasa, Phys. Rev. E 85, 031151 (2012).
- K. Lindenberg and V. Seshadri, Physica A 109, 483 (1981); K. Lindenberg and E. Cortés, ibid. 126, 489 (1984).
- D. Barik, D. Banerjee, and D. S. Ray, in Progress in Chemical Physics Research, Vol. 1, edited by A. N. Linke (Nova, New York, 2006).
- D. Barik and D. S. Ray, J. Stat. Phys. 120, 339 (2005).
- E. P. Wigner, Phys. Rev. 40, 749 (1932); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).
- S. K. Banik, B. C. Bag, and D. S. Ray, Phys. Rev. E 65, 051106 (2002).
- P. K. Ghosh, D. Barik, and D. S. Ray, Phys. Rev. E 71, 041107 (2005); D. Banerjee, B. C. Bag, S. K. Banik, and D. S. Ray, J. Chem. Phys. 120, 8960 (2004).
- D. Barik, S. K. Banik, and D. S. Ray, J. Chem. Phys. 119, 680 (2003); D. Barik, B. C. Bag, and D. S. Ray, ibid. 119, 12973 (2003).
- D. Barik and D. S. Ray, J. Chem. Phys. 121, 1681 (2004).
- P. K. Ghosh, D. Barik, and D. S. Ray, Phys. Lett. A 342, 12 (2005).
- P. K. Ghosh, D. Barik, B. C. Bag, and D. S. Ray, J. Chem. Phys. 123, 224104 (2005).
- W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1990).
- E. T. Jaynes, in Statistical Physics, edited by W. K. Ford (Benjamin, New York, 1963).
- A. Katz, Statistical Mechanics (Freemann, San Francisco, 1967).
- A. Baura, M. K. Sen, and B. C. Bag, Phys. Rev. E 82, 041102 (2010).
- B. R. Frieden, Opt. Lett. 14, 199 (1989).
- M. Munowitz, Coherence and NMR (Wiley, New York, 1988).
- S. S. Sinha, D. Mondal, B. C. Bag, and D. S. Ray, Phys. Rev. E 82, 051125 (2010); S. S. Sinha, A. Ghosh, and D. S. Ray, ibid. 84, 031118 (2011); S. S. Sinha, D. Mondal, B. C. Bag, and D. S. Ray, ibid. 84, 041113 (2011); J. Chem. Phys. 134, 094114 (2011).
- S. S. Sinha, A. Ghosh, and D. S. Ray, Phys. Rev. E 87, 042112 (2013).