Equilibrium and transient thermodynamics: A unified dissipaton-space approach

Abstract

This work presents a unified dissipaton-equation-of-motion (DEOM) theory and its evaluations on the Helmholtz free energy change due to the isotherm mixing of two isolated subsystems. One is a local impurity, and the other is a nonlocal Gaussian bath. DEOM constitutes a fundamental theory for such open quantum mixtures. To complete the theory, we also construct the imaginary-time DEOM formalism via an analytical continuation of dissipaton algebra, which would be limited to equilibrium thermodynamics. On the other hand, the real-time DEOM deals with both equilibrium structural and nonequilibrium dynamic properties. Its combination with the thermodynamic integral formalism would be a viable and accurate means to both equilibrium and transient thermodynamics. As illustrations, we report the numerical results on a spin-boson system, with elaborations on the underlying anharmonic features, the thermodynamic entropy vs the von Neumann entropy, and an indication of “solvent-cage” formation. Beside the required asymptotic equilibrium properties, the proposed transient thermodynamics also supports the basic spontaneity criterion.

Numerically “exact” simulations of entropy production in the fully quantum regime: Boltzmann entropy vs von Neumann entropy

“…The differences between the Boltzmann and von Neumann cases become larger as the system-bath coupling strengthens, in particular, at low temperatures (see also Ref. 78), but the overall profiles for the two results are similar. This is because we calculated both entropies using the reduced density matrix of the main system obtained from the HEOM, and thus, the effects of the non-perturbative system-bath interaction were indirectly taken into account in the von Neumann case.…”

Temperature-dependence of the subdivision potential in nanothermodynamics

“…It is reasonable to render the difference arises from that the thermodynamic limit is not satisfied for small systems. Thermodynamic integration -Now, we apply the thermodynamic integration for the free energy F , as done in our previous works [11,12]. Consider a λ-augmented form of Eq.…”

“…( 18), we have defined ∆S therm/vN (T ) ≡ S therm/vN (T ; λ = 1) − S therm/vN (T ; λ = 0) and used the equality S vN (T ; λ = 0) = S therm (T ; λ = 0) due to the canonicity in the absence of system-bath interactions. Numerically, all these quantities can be computed via the dissipaton-equation-of-motion method (λ-dynamics formalism or imaginary-time formalism) [11][12][13], which is a second quantization generalization of the well-known hierarachical equations of motion, serving as a rigid approach to the dynamics of a specific system coupled to the Gaussian environments [14][15][16][17]. Example -As an example, we consider a spin-boson model…”

“…FIG.2: Tempature-dependenece of the subvivision potential. Parameters are taken in accordance to that in Ref [11]…”

A nonequilibrium statistical quasi-particles thermofield theory

“…As for an open quantum system, thermal effects arise from its coupled environments and play important roles in determining the system and correlated systemenvironment properties. These properties are closely related to such as thermodynamics [1][2][3] and transport [4][5][6] in quantum impurity systems. On the other hand, environmental noises are inevitable in various realms of physics.…”