A strengthened Lindblad inequality has been proved. We have applied this result to prove a generalized $H$ theorem in nonequilibrium thermodynamics. Information processing also can be considered as some thermodynamic process. From this point of view we have proved a strengthened data processing inequality in quantum information theory.A strengthened Lindblad inequality has been proved. We have applied this result to prove a generalized $H$ theorem in nonequilibrium thermodynamics. Information processing also can be considered as some thermodynamic process. From this point of view we have proved a strengthened data processing inequality in quantum information theory.

arXiv:cond-mat/9809127Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJul 1, 19983 citations

An application of the Lieb-Thirring inequality in quantum information theory

Christopher King

International Congress on Mathematical Physics (ICMP)Mar 1, 200611 citations

Variation on the theme of Jarzynski's inequality

Dani R. Castellanos, Petr Jizba

The Jarzynski equality, which relates equilibrium free-energy difference to an average of non-equilibrium work, plays a central role in modern non-equilibrium statistical thermodynamics. In this paper, we study a weaker consequence of this relation, known as Jarzynski's inequality, which can be formally obtained from the Jarzynski equality via Jensen's inequality. We identify and analyze several extensions of Jarzynski's inequality that go beyond its direct derivation from the Jarzynski equality. In particular, we consider chemical systems both in the linear-response regime and away from linear thermodynamics. Furthermore, by employing functional-integral techniques, we extend Jarzynski's inequality to many-body statistical systems described by quantum field theory. Salient issues, such as connections of the Jarzynski inequality with the maximum work theorem and the Landau--Lifshitz theory of fluctuations, are also discussed.The Jarzynski equality, which relates equilibrium free-energy difference to an average of non-equilibrium work, plays a central role in modern non-equilibrium statistical thermodynamics. In this paper, we study a weaker consequence of this relation, known as Jarzynski's inequality, which can be formally obtained from the Jarzynski equality via Jensen's inequality. We identify and analyze several extensions of Jarzynski's inequality that go beyond its direct derivation from the Jarzynski equality. In particular, we consider chemical systems both in the linear-response regime and away from linear thermodynamics. Furthermore, by employing functional-integral techniques, we extend Jarzynski's inequality to many-body statistical systems described by quantum field theory. Salient issues, such as connections of the Jarzynski inequality with the maximum work theorem and the Landau--Lifshitz theory of fluctuations, are also discussed.

cond-mat.stat-mechCross-listedarXiv:2601.01644Jan 6, 2026

Kinetic and thermodynamic temperatures in quantum systems

Alessio Gagliardi, Alessandro Pecchia, Aldo Di Carlo

In this work we present a formalism to describe non equilibrium conditions in systems with a discretized energy spectrum, such as quantum systems. We develop a formalism based on a combination of Gibbs-Shannon entropy and information thermodynamics that arrives to a generalization of the De-Brujin identity applicable to discrete and non-symmetric distributions. This allows to define the concept of a thermodynamic temperature with a different, albeit complementary meaning to the equilibrium kinetic temperature of a system. The theory is applied to Bosonic and Fermionic cases represented by an harmonic oscillator and a single energy state, respectively. We show that the formalism correctly recovers known results at equilibrium, then we demonstrate an application to a genuine non equilibrium state: a coherent quantum oscillator.In this work we present a formalism to describe non equilibrium conditions in systems with a discretized energy spectrum, such as quantum systems. We develop a formalism based on a combination of Gibbs-Shannon entropy and information thermodynamics that arrives to a generalization of the De-Brujin identity applicable to discrete and non-symmetric distributions. This allows to define the concept of a thermodynamic temperature with a different, albeit complementary meaning to the equilibrium kinetic temperature of a system. The theory is applied to Bosonic and Fermionic cases represented by an harmonic oscillator and a single energy state, respectively. We show that the formalism correctly recovers known results at equilibrium, then we demonstrate an application to a genuine non equilibrium state: a coherent quantum oscillator.

arXiv:1305.2104May 9, 20130 citations

Thermodynamic and Informational Entropies in Quantum Mechanics

Francis Fer

Springer eBooksJan 1, 19870 citations

Aspects of non-equilibrium quantum statistical mechanics: An introduction

William C. Schieve

Springer eBooksOct 20, 20053 citations

A strengthened Lindblad inequality has been proved. We have applied this result to prove a generalized

H

theorem in nonequilibrium thermodynamics. Information processing also can be considered as some thermodynamic process. From this point of view we have proved a strengthened data processing inequality in quantum information theory.