arXiv subjects

Andrés Vallejo

Publications and source records attributed to Andrés Vallejo.

12 recordsLinked to original sources

arXiv2026

Entropy-based analysis of single-qubit Otto and Carnot heat engines

From an entropy-based formulation of the first law of thermodynamics in the quantum regime, we investigate the performance of Otto-like and Carnot-like engines for a single-qubit working medium. Within this framework, the first law includes an additional contribution -- coherence work -- that quantifies the energetic cost of deviating the quantum trajectory from its natural unitary evolution. We focus on the efficiency of the heat-to-coherence work conversion and show that the Carnot cycle achieves the classical Carnot efficiency, while the performance of the Otto cycle is upper-bounded by the Carnot efficiency corresponding to the extreme temperatures of the cycle. We identify entropy generation during the isochoric stages as the key source of irreversibility limiting the Otto cycle's efficiency.

quant-ph↗

arXiv2025

Evolution of expected values in open quantum systems

We derive a generalization of Ehrenfest theorem valid for open quantum systems. From this result, we identify three contributions to the evolution of expected values: i) the explicit time dependence of the observable, ii) the incompatibility between the observable and an operator which plays the role of an effective Hamiltonian, and iii) entropy changes. Considering the local Hamiltonian as the observable, and adopting a specific interpretation of the nature of thermal interactions, we obtain an alternative version of the first law of thermodynamics. Within this framework, we show that in some cases the power performed by the system can be considered as a quantum observable. As an application, the pure dephasing process is reinterpreted from this perspective.

quant-ph↗

arXiv2023

Which is greater: $\boldsymbol{e^π}$ or $\boldsymbol{π^{e}}$? An unorthodox solution to a classic puzzle

The question of the title is a famous puzzle in the field of recreational mathematics, and can be addressed by several approaches. A compilation of solutions, some of them very ingenious, can be found in [1]. In this contribution we present an alternative solution based on the second law of thermodynamics. The method can be extended to derive a more general result involving the exponential function.

physics.class-ph↗

arXiv2023

Finding and improving bounds of real functions by thermodynamic arguments

The possibility of stating the second law of thermodynamics in terms of the increasing behaviour of a physical property establishes a connection between that branch of physics and the theory of algebraic inequalities. We use this connection to show how some well-known inequalities such as the standard bounds for the logarithmic function or generalizations of Bernoulli's inequality can be derived by thermodynamic methods. Additionally, we show that by comparing the global entropy production in processes implemented with decreasing levels of irreversibility but subject to the same change of state of one particular system, we can find progressively better bounds for the real function that represents the entropy variation of the system. As an application, some new families of bounds for the function $\log(1+x)$ are obtained by this method.

cond-mat.stat-mech↗

arXiv2023

A diagrammatic representation of entropy production

We introduce a natural way of visualizing the entropy production in heat transfer processes between a system and a thermal reservoir. This representation is particularly useful to highlight the asymmetric character of the heating and cooling processes, when they are analyzed from the second-law perspective.

cond-mat.stat-mech↗

arXiv2023

Irreversibility of sudden processes: Compression versus expansion in perfect gases

We focus on the study of the processes undergone by a perfect gas when the external pressure is suddenly modified. The analysis shows that, from the second law perspective, there is a non-evident asymmetry between the processes of compression and expansion between the same pressures, which is manifested through different levels of entropy production. If the system remains in contact with a thermal reservoir during the processes this asymmetry is remarkable, since while entropy grows linearly with the relative change of pressure during the compression, the relation between those variables is logarithmic during the expansion.

physics.class-ph↗

arXiv2021

Qubit thermodynamics far from equilibrium: two perspectives about the nature of heat and work in the quantum regime

Considering an entropy-based division of energy transferred into heat and work, we develop an alternative theoretical framework for the thermodynamic analysis of two-level systems. When comparing these results with those obtained under the standard definitions of these quantities, we observe the appearance of a new term of work, which represents the energy cost of rotating the Bloch vector in presence of the external field that defines the local Hamiltonian. Additionally, we obtain explicit expressions for the temperature, the heat capacity and the internal entropy production of the system in both paradigms. In order to illustrate our findings we study, from both perspectives, matter-radiation interaction processes for two different systems.

quant-ph↗

arXiv2020

Temperature of a finite-dimensional quantum system

A general expression for the temperature of a finite-dimensional quantum system is deduced from thermodynamic arguments. At equilibrium, this magnitude coincides with the standard thermodynamic temperature. Furthermore, it is well-defined even far from equilibrium. Explicit formulas for the temperature of two and three-dimensional quantum systems are presented, and some additional relevant aspects of this quantity are discussed.

quant-ph↗

arXiv2020

Entropy production in the quantum walk

We explore the notion of generated entropy in open quantum systems. We focus on the study of the discrete-time quantum walk on the line, from the entropy production perspective. We argue that the evolution of the coin can be modeled as an open two-level system that exchanges energy with the lattice at some effective temperature that depends on the initial state. The entropy balance shows that there is a positive entropy production during the evolution, in accordance with the second law of thermodynamics.

quant-ph↗

arXiv2020

Out-of-equilibrium quantum thermodynamics in the Bloch sphere: temperature and internal entropy production

An explicit expression for the temperature of an open two-level quantum system is obtained as a function of local properties, under the hypothesis of weak interaction with the environment. This temperature is defined for both equilibrium and out-of-equilibrium states, and coincides with the environment temperature if the system reaches thermal equilibrium with a heat reservoir. Additionally, we show that within this theoretical framework the total entropy production can be partitioned into two contributions: one due to heat transfer, and another, associated to internal irreversibilities, related to the loss of internal coherence by the qubit. The positiveness of the heat capacity is established, as well as its consistency with the well known results at thermal equilibrium. We apply these concepts to two different systems, and show that they behave in analogous ways as their classical counterparts.

quant-ph↗

arXiv2018

Initial-state-dependent thermalization in open qubits

We study, from a thermodynamic perspective, the equilibrium states of a qubit interacting with an arbitrary environment of dimension N>>2. We show that even in presence of memory about the initial state, in some cases the qubit can be considered in a thermal state characterized by an entanglement Hamiltonian, which encodes the effects of the environment, and an initial-state- dependent entanglement temperature that measures the degree of entanglement generated between the system and its environment. Geometrical aspects of the thermal states are studied, and the results are confirmed for the concrete case of the Quantum Walk on the Line.

quant-ph↗

arXiv2015

Relation between the usual and the entanglement temperature, in a simple quantum system

We develop a thermodynamical theory to describe the behavior of the entanglement between a single two-level atom with a single mode of the electromagnetic field. The resonant Jaynes-Cummings model is used to study both the entanglement thermodynamics, in particular the entanglement temperature, and its connection with the average number of photons in the optical cavity. We find that this entanglement temperature has a strong dependence with the initial conditions of the atom. We show that the entanglement temperature between the photons and the atom defined in this work is the same temperature obtained within the Jaynes-Cummings model at finite temperature developed in the Thermo-Field Dynamics formalism.

quant-ph↗