Microscopic non-equilibrium structure and dynamical model of entropy flow

Renato Ascoli, R. Urigu

Tomio Yamakoshi Petrosky

Recent developments on the complex spectral representation of the evolution operators have shown that irreversibility is a rigorous dynamical process that takes place outside the Hilbert space for non‐integrable systems, both classical and quantum. Irreversibility is a direct consequence of microscopic dynamical processes associated with resonance singularities, rather than our incomplete knowledge. We discuss the excitation process of a quantum unstable particle by scattering of a wave packet. Using complex eigenstates of the Hamiltonian one may construct a microscopic dynamical entropy (or H function) without any approximation. In order to have scattering, one has to target the wave packet to the particle. This introduces a nonlocal pre‐collisional correlation giving a low dynamical entropy. During the moment the excited particle is created, there appears an entropy flow from the field to the particle. This lowers the particle component of the entropy, even though the total entropy production is always positive. This implies that the excitation of the particle may be considered as the construction of a non‐equilibrium structure due to entropy flow.

J. M. Z. Choquehuanca

Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this thesis, we explore different ways to describe quantum thermodynamics, using two main approaches: one based on entropy and the other on ergotropy. First, we introduce a generalized approach to quantify non-Markovianity through the breakdown of monotonicity in thermodynamic functions. In this context, the entropy-based heat flow serves as a practical tool to witness and measure quantum memory in unital maps that do not reverse the sign of the internal energy. Next, we analyze the dynamics of ergotropy in open qubits under both Markovian and non-Markovian evolutions. We identify phenomena such as freezing and sudden death of ergotropy, and we establish an analytical relation between the change in ergotropy and the environment-induced work . This provides a clear physical interpretation for the additional term in the first law in the entropy-based formulation. Finally, we propose an ergotropy-based thermodynamic formulation, in which heat is reinterpreted in terms of the change of the passive state associated with the density operator governing the quantum dynamics. This approach allows one to measure non-Markovianity of unital maps more generally and accurately than the entropy-based heat flow. This advantage comes from the direct link between heat and von Neumann entropy, a property ensured by invariance under passive transformations. Moreover, the out-of-equilibrium temperature naturally remains non-negative, similarly to equilibrium thermodynamics.

Gian Paolo Beretta, Gian Paolo Beretta, Ahmed F. Ghoniem +1 more

First, we briefly address the questions: “Is entropy defined for non‐equilibrium states?” and “Is entropy an intrinsic property of matter?”. Then, we focus on: “Is irreversibility an intrinsic feature of microscopic dynamics?” We answer this question by discussing the structure and main features of the nonlinear evolution equation proposed by this author to capture precisely how the essence of the Second Law of Thermodynamics could be embedded at the most fundamental level of description, i.e., the quantum level. The nonlinear equation generates a dynamical group providing a unique deterministic description of irreversible, conservative relaxation towards equilibrium from any non‐equilibrium state, following a locally constrained, steepest entropy ascent, maximal entropy generation path. The Hatsopoulos‐Keenan statement of the Second Law emerges as a general theorem about the Lyapunov stability of the equilibrium states of the proposed evolution equation. An appendix gives mathematical details and outlines other important theorems.

Masuo Suzuki

Seiji Miyashita