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.
Highlights
Thermodynamics is the phenomenological theory of heat and work
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
Summary
Right panel: In the broken regime quantum work can no longer be determined by the two-time energy measurement as 〈 ψ, gψ〉 can be both positive and negative. To make the spectrum of (26) real we set λt to be purely imaginary (λt → iλt); and without any loss of generality we choose γ = 1 This corresponds to the following parameters E1,2 = 0, Γ 1,2 = ± λt, and q = γ = 1 for the hybrid light–matter system of quasiparticles investigated in Ref. 6. Such systems are formed as a result of a strong interaction between excitons and photons in a semiconductor microcavity[53]. Quantum work can still be defined, and we have shown that the second law still holds for all pseudo-hermitian systems
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