title: Thermodynamic framework for the ground state of a simple quantum system.
abstract: The ground state of a two-level system (associated with probabilities p and 1-p, respectively) defined by a general Hamiltonian H[over ̂]=H[over ̂]_{0}+λV[over ̂] is studied. The simple case characterized by λ=0, whose Hamiltonian H[over ̂]_{0} is represented by a diagonal matrix, is well established and solvable within Boltzmann-Gibbs statistical mechanics; in particular, it follows the third law of thermodynamics, presenting zero entropy (S_{BG}=0) at zero temperature (T=0). Herein it is shown that the introduction of a perturbation λV[over ̂] (λ>0) in the Hamiltonian may lead to a nontrivial ground state, characterized by an entropy S[p] (with S[p]≠S_{BG}[p]), if the Hermitian operator V[over ̂] is represented by a 2×2 matrix, defined by nonzero off-diagonal elements V_{12}=V_{21}=-z, where z is a real positive number. Hence, this new term in the Hamiltonian, presenting V_{12}≠0, may produce physically significant changes in the ground state, and especially, it allows for the introduction of an effective temperature θ (θ∝λz), which is shown to be a parameter conjugated to the entropy S. Based on this, one introduces an infinitesimal heatlike quantity, δQ=θdS, leading to a consistent thermodynamic framework, and by proposing an infinitesimal form for the first law, a Carnot cycle and thermodynamic potentials are obtained. All results found are very similar to those of usual thermodynamics, through the identification T↔θ, and particularly the form for the efficiency of the proposed Carnot Cycle. Moreover, S also follows a behavior typical of a third law, i.e., S→0, when θ→0.
authors.affiliation: Departamento de Física, Universidade Federal de Sergipe, 49100-000 São Cristovão - SE, Brazil.|National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ, Brazil.
authors.forename: Andre M C
authors.initials: AM
authors.lastname: Souza
authors.affiliation: National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ, Brazil.|Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ, Brazil.
authors.forename: Fernando D
authors.initials: FD
authors.lastname: Nobre