PMID- 33353341
OWN - NLM
STAT- PubMed-not-MEDLINE
LR  - 20201223
IS  - 1089-7690 (Electronic)
IS  - 0021-9606 (Linking)
VI  - 153
IP  - 23
DP  - 2020 Dec 21
TI  - Numerically "exact" simulations of entropy production in the fully quantum 
      regime: Boltzmann entropy vs von Neumann entropy.
PG  - 234107
LID - 10.1063/5.0033664 [doi]
AB  - We present a scheme to evaluate thermodynamic variables for a system coupled to a 
      heat bath under a time-dependent external force using the quasi-static Helmholtz 
      energy from the numerically "exact" hierarchical equations of motion (HEOM). We 
      computed the entropy produced by a spin system strongly coupled to a 
      non-Markovian heat bath for various temperatures. We showed that when changes to 
      the external perturbation occurred sufficiently slowly, the system always reached 
      thermal equilibrium. Thus, we calculated the Boltzmann entropy and the von 
      Neumann entropy for an isothermal process, as well as various thermodynamic 
      variables, such as changes in internal energies, heat, and work, for a system in 
      quasi-static equilibrium based on the HEOM. We found that although the 
      characteristic features of the system entropies in the Boltzmann and von Neumann 
      cases as a function of the system-bath coupling strength are similar, those for 
      the total entropy production are completely different. The total entropy 
      production in the Boltzmann case is always positive, whereas that in the von 
      Neumann case becomes negative if we chose a thermal equilibrium state of the 
      total system (an unfactorized thermal equilibrium state) as the initial state. 
      This is because the total entropy production in the von Neumann case does not 
      properly take into account the contribution of the entropy from the system-bath 
      interaction. Thus, the Boltzmann entropy must be used to investigate entropy 
      production in the fully quantum regime. Finally, we examined the applicability of 
      the Jarzynski equality.
FAU - Sakamoto, Souichi
AU  - Sakamoto S
AD  - Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 
      606-8502, Japan.
FAU - Tanimura, Yoshitaka
AU  - Tanimura Y
AUID- ORCID: 000000027913054X
AD  - Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 
      606-8502, Japan.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - J Chem Phys
JT  - The Journal of chemical physics
JID - 0375360
SB  - IM
EDAT- 2020/12/24 06:00
MHDA- 2020/12/24 06:01
CRDT- 2020/12/23 05:29
PHST- 2020/12/23 05:29 [entrez]
PHST- 2020/12/24 06:00 [pubmed]
PHST- 2020/12/24 06:01 [medline]
AID - 10.1063/5.0033664 [doi]
PST - ppublish
SO  - J Chem Phys. 2020 Dec 21;153(23):234107. doi: 10.1063/5.0033664.