Non-hermitian quantum thermodynamics

Abstract

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions, namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.

Time-dependent PT -symmetric quantum mechanics in generic non-Hermitian systems

“…The JE relates free energy differences between two equilibrium states to the exponentiated work averaged over an ensemble of trajectories. It is one of the celebrated results in thermodynamics [42,43] and was recently generalized to PT -symmetric systems [32,37]. Here, we further extend JE to generic non-Hermitian systems.…”

“…(22), before the second measurement associated with H(τ ) is performed at t = τ . For this process, the probability that the two outcomes ε m (0) (at t = 0) and ε n (τ ) (at t = τ ) jointly occur reads [32,37] P [ε m (0), ε n (τ )] = tr Π n (τ )U(τ )Π m (0)ρ S (0)Π m (0)U −1 (τ ) . (49) Here, U(τ ) := T exp[−i τ 0 H(t)dt] is the evolution operator, where T denotes the time-ordering operator.…”

Crooks fluctuation theorem in ${\mathscr{PT}}$-symmetric quantum mechanics

“…In the recent work [18,19], the authors proved that the quantum Jarzynski equality can be readily generalised to non-Hermitian quantum systems with unbroken  -symmetry, by adopting a modified unitary time-evolution operator suitable for the formalism of non-Hermitian quantum mechanics. However, to the best of our knowledge, the more general Crooks fluctuation theorem has not been proved in the  -symmetric quantum mechanical framework, and this is the purpose of our present work.…”

Non-Hermitian heat engine with all-quantum-adiabatic-process cycle

“…Moreover, via constructing a QHE which is a two-level quantum system and undergoes quantum adiabatic process and energy exchanges with heat baths at different stages in a work cycle, some important aspects of the second law of thermodynamics have been clarified by Kieu [30]. Very recently, many other investigations have been carried out and demonstrated about the Carnot statement of the second law of thermodynamics and the quantum Jarzynski equality in quantum systems described by pseudo-Hermitian Hamiltonians [31].…”