The third law of thermodynamics in open quantum systems

Abhay Shastry, Yiheng Xu, Charles A. Stafford

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish (US)
Article number064115
JournalJournal of Chemical Physics
Issue number6
StatePublished - Aug 14 2019

ASJC Scopus subject areas

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


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