The physics and mathematics of the second law of thermodynamics (Physics Reports 310 (1999) 1–96)☆

  title={The physics and mathematics of the second law of thermodynamics (Physics Reports 310 (1999) 1–96)☆},
  author={Elliott H. Lieb and Jakob Yngvason},
  journal={Physics Reports},

The Mathematics of the Second Law of Thermodynamics

The essence of the second law is the ‘entropy principle’ which states that adiabatic processes can be quantified by an entropy function on the space of all equilibrium states, whose increase is a

Thermodynamics: The Unique Universal Science

The history of thermodynamics is traced from its classical to its postmodern forms, and a tutorial and didactic exposition of thermodynamic principles as it pertains to some of the deepest secrets of the universe are presented.

A Pedagogical Approach to Obtain the Combined First and Second Law of Thermodynamics from Classical Statistical Mechanics

The combined first and second law of thermodynamics for a closed system is written as dE=TdS - PdV, where E is the internal energy, S is the entropy, V is the volume, T is the temperature, and P is

Comment on the law of entropy increase in thermodynamics

A common formulation of the law of increase of entropy, found in textbooks on thermodynamics, states that in a process taking place in a completely isolated system the entropy of the final

The entropy concept for non-equilibrium states

  • E. LiebJ. Yngvason
  • Physics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2013
The conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties, but it is shown that one can define two entropy functions, called S− and S+, which, taken together, delimit the range of adiabatic processes that can occur between non-equilibrium states.

Quantum Mechanics Entropy and a Quantum Version of the H-Theorem

Entropy is a fundamental concept which emerged along with other ideas during the development of thermodynamics and statistical mechanics Landau and Lifshitz (1978); Lieb and Yngvason (1999). Entropy

Unitary Proof of the Second Law of Thermodynamics

In this chapter, we review how to derive the second law of thermodynamics for systems that obey quantum mechanics at the microscopic level. Starting with the statement of the second law, we derive it

On the foundations of thermodynamics

On the basis of new, concise foundations, this paper establishes the four laws of thermodynamics, the Maxwell relations, and the stability requirements for response func- tions, in a form applicable

Entropy and the Second Law of Thermodynamics—The Nonequilibrium Perspective

An alternative to the Carnot-Clausius approach for introducing entropy and the second law of thermodynamics is outlined that establishes entropy as a nonequilibrium property from the onset. Five

New definitions of thermodynamic temperature and entropy not based on the concepts of heat and thermal reservoir

From a new rigorous formulation of the general axiomatic foundations of thermodynamics we derive an operational definition of entropy that responds to the emergent need in many technological



Entropy concept and ordering of states. I

In an earlier paper it was proposed to regard the Second Law of Thermodynamics, in the form of the Principle ofCarathéodory, primarily as an essential link in an argument leading directly to the

The second law of thermodynamics and stability

Abstract : There are several indications pointing to an intimate relationship between the second law of thermodynamics and 'stability'. Here I attempt to establish a different connection between

On the redundancy of the zeroth law of thermodynamics

Expositions of classical thermodynamics frequently include the so-called zeroth law amongst its 'fundamental principles'. It is shown here that, given only the first law and the second law (the

Thermodynamics and an Introduction to Thermostatistics

GENERAL PRINCIPLES OF CLASSICAL THERMODYNAMICS. The Problem and the Postulates. The Conditions of Equilibrium. Some Formal Relationships, and Sample Systems. Reversible Processes and the Maximum Work

The Second Law of Thermodynamics

Is it not true that the Second Law of Thermodynamics is contradicted by the known facts of diffusion? When, for instance, masses of hydrogen and nitrogen are separated by a palladium partition, a

An axiomatic approach to classical thermodynamics

  • J. Boyling
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1972
Carathéodory’s formulation of classical thermodynamics is cast into a mathematically rigorous form, in which such well-known results as the existence of entropy and of (positive) absolute

Thermodynamics based on the Hahn-Banach Theorem: The Clausius inequality

ed, permit analysis of those theories within a common framework. In the spirit of work by COLEMAN and Ow~N, we seek to develop a " theory of theories" which, for example, makes possible isolation of

A First Course in the Mathematical Foundations of Thermodynamics

I Classical Thermodynamicsl.- 1. Homogeneous Fluid Bodies.- 2. The First Law Energy.- 3. The Second Law Entropy.- 4. A General Efficiency Estimate.- II Systems with Perfect Accessibility.- 1.

Convexity in the Theory of Lattice Gases

In this book, Robert Israel considers classical and quantum lattice systems in terms of equilibrium statistical mechanics. He is especially concerned with the characterization of