### Abstract

We consider open quantum systems consisting of a finite system of independent fermions with arbitrary Hamiltonian coupled to one or more equilibrium fermion reservoirs (which need not be in equilibrium with each other). A strong form of the third law of thermodynamics, S(T) → 0 as T → 0, is proven for fully open quantum systems in thermal equilibrium with their environment, defined as systems where all states are broadened due to environmental coupling. For generic open quantum systems, it is shown that S(T) → g ln 2 as T → 0, where g is the number of localized states lying exactly at the chemical potential of the reservoir. For driven open quantum systems in a nonequilibrium steady state, it is shown that the local entropy Sx;T→0 as T(x) → 0, except for cases of measure zero arising due to localized states, where T(x) is the temperature measured by a local thermometer.

Original language | English (US) |
---|---|

Article number | 064115 |

Journal | Journal of Chemical Physics |

Volume | 151 |

Issue number | 6 |

DOIs | |

State | Published - Aug 14 2019 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*151*(6), [064115]. https://doi.org/10.1063/1.5100182

**The third law of thermodynamics in open quantum systems.** / Shastry, Abhay; Xu, Yiheng; Stafford, Charles A.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 151, no. 6, 064115. https://doi.org/10.1063/1.5100182

}

TY - JOUR

T1 - The third law of thermodynamics in open quantum systems

AU - Shastry, Abhay

AU - Xu, Yiheng

AU - Stafford, Charles A

PY - 2019/8/14

Y1 - 2019/8/14

N2 - We consider open quantum systems consisting of a finite system of independent fermions with arbitrary Hamiltonian coupled to one or more equilibrium fermion reservoirs (which need not be in equilibrium with each other). A strong form of the third law of thermodynamics, S(T) → 0 as T → 0, is proven for fully open quantum systems in thermal equilibrium with their environment, defined as systems where all states are broadened due to environmental coupling. For generic open quantum systems, it is shown that S(T) → g ln 2 as T → 0, where g is the number of localized states lying exactly at the chemical potential of the reservoir. For driven open quantum systems in a nonequilibrium steady state, it is shown that the local entropy Sx;T→0 as T(x) → 0, except for cases of measure zero arising due to localized states, where T(x) is the temperature measured by a local thermometer.

AB - We consider open quantum systems consisting of a finite system of independent fermions with arbitrary Hamiltonian coupled to one or more equilibrium fermion reservoirs (which need not be in equilibrium with each other). A strong form of the third law of thermodynamics, S(T) → 0 as T → 0, is proven for fully open quantum systems in thermal equilibrium with their environment, defined as systems where all states are broadened due to environmental coupling. For generic open quantum systems, it is shown that S(T) → g ln 2 as T → 0, where g is the number of localized states lying exactly at the chemical potential of the reservoir. For driven open quantum systems in a nonequilibrium steady state, it is shown that the local entropy Sx;T→0 as T(x) → 0, except for cases of measure zero arising due to localized states, where T(x) is the temperature measured by a local thermometer.

UR - http://www.scopus.com/inward/record.url?scp=85070736288&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070736288&partnerID=8YFLogxK

U2 - 10.1063/1.5100182

DO - 10.1063/1.5100182

M3 - Article

AN - SCOPUS:85070736288

VL - 151

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 6

M1 - 064115

ER -