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The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws…

Statistical Mechanics · Physics 2023-11-21 Ralph V. Chamberlin

We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function…

Statistical Mechanics · Physics 2015-05-13 H. -H. Hasegawa , J. Ishikawa , K. Takara , D. J. Driebe

The relationship between thermodynamics and statistical physics is valid in the thermodynamic limit - when the number of particles becomes very large. Here, we study thermodynamics in the opposite regime - at both the nano scale, and when…

Quantum Physics · Physics 2014-10-28 Michał Horodecki , Jonathan Oppenheim

To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…

Statistical Mechanics · Physics 2007-05-23 V. V. Ryazanov , S. G. Shpyrko

The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different…

Mathematical Physics · Physics 2007-05-23 Walid K. Abou Salem

The recursive property of entropy is well known in information theory; however, the concept is underutilized in thermodynamics, despite being the field where the concept of entropy originated. The zentropy approach is built on this idea,…

Statistical Mechanics · Physics 2026-05-19 Luke Allen Myers , Nigel Lee En Hew , Shun-Li Shang , Zi-Kui Liu

The entropy production is commonly interpreted as measuring the distance from equilibrium. However, this explanation lacks a rigorous description due to the absence of a natural equilibrium measure. The present analysis formalizes this…

Statistical Mechanics · Physics 2025-10-23 David Andrieux

We generalize stochastic thermodynamics to include information reservoirs. Such information reservoirs, which can be modeled as a sequence of bits, modify the second law. For example, work extraction from a system in contact with a single…

Statistical Mechanics · Physics 2014-11-17 Andre C. Barato , Udo Seifert

The thermal response of nonequilibrium systems requires the knowledge of concepts that go beyond entropy production. This is showed for systems obeying overdamped Langevin dynamics, either in steady states or going through a relaxation…

Statistical Mechanics · Physics 2016-08-31 Gianmaria Falasco , Marco Baiesi

Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics…

Statistical Mechanics · Physics 2021-07-07 Marco Baldovin , Stefano Iubini , Roberto Livi , Angelo Vulpiani

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…

Quantum Physics · Physics 2025-12-02 J. M. Z. Choquehuanca

Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, $\sum_k p_k\ln(p_k/p_k^*)$, has a natural role in the energetics of equilibrium and…

Mathematical Physics · Physics 2007-05-23 Hong Qian

Thermodynamic principles governing energy and information are important tools for a deeper understanding and better control of quantum systems. In this work, we experimentally investigate the interplay of the thermodynamic costs and…

For macroscopic systems, the second law of thermodynamics establishes an inequality between the amount of work performed on a system in contact with a thermal reservoir, and the change in its free energy. For microscopic systems, this…

Statistical Mechanics · Physics 2010-02-08 Eliran Boksenbojm , Bram Wynants , Christopher Jarzynski

We consider the thermodynamic approach to the description of economic systems and processes. The first and second laws of thermodynamics as applied to economic systems are derived and analyzed. It is shown that there is a deep analogy…

General Finance · Quantitative Finance 2021-02-03 Sergey Rashkovskiy

The Clausius inequality (CI) form of the second law of thermodynamics relates information changes (entropy) to changes in the first moment of the energy (heat and indirectly also work). Are there similar relations between other moments of…

Quantum Physics · Physics 2017-09-27 Raam Uzdin

Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…

Statistical Mechanics · Physics 2025-10-31 O. B. Ericok , J. K. Mason

Equilibrium thermodynamics describes the energy exchange of a body with its environment. Here, we describe the global energy exchange of an ideal gas in the Coutte flow in a thermodynamic-like manner. We derive a fundamental relation…

Statistical Mechanics · Physics 2023-07-31 Karol Makuch , Konrad Giżyński , Robert Hołyst , Anna Maciołek , Paweł J. Żuk

We examine stochastic processes that are used to model nonequilibrium processes (e.g, pulling RNA or dragging colloids) and so deliberately violate detailed balance. We argue that by combining an information-theoretic measure of…

Statistical Mechanics · Physics 2009-11-13 R. A. Blythe

For a single enzyme or molecular motor operating in an aqueous solution of non-equilibrated solute concentrations, a thermodynamic description is developed on the level of an individual trajectory of transitions between states. The concept…

Statistical Mechanics · Physics 2012-05-21 Udo Seifert
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