The Physics and Mathematics of the Second Law of Thermodynamics
arXiv:cond-mat/9708200 · doi:10.1016/S0370-1573(98)00082-9
Abstract
The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy constructed here is defined only for equilibrium states and no attempt is made to define it otherwise. Statistical mechanics does not enter these considerations. One of the main concepts that makes everything work is the comparison principle (which, in essence, states that given any two states of the same chemical composition at least one is adiabatically accessible from the other) and we show that it can be derived from some assumptions about the pressure and thermal equilibrium. Temperature is derived from entropy, but at the start not even the concept of `hotness' is assumed. Our formulation offers a certain clarity and rigor that goes beyond most textbook discussions of the second law.
93 pages, TeX, 8 eps figures. Updated, published version. A summary appears in Notices of the Amer. Math. Soc. 45 (1998) 571-581, math-ph/9805005
Cited by in corpus (186)
- The role of quantum information in thermodynamics --- a topical review
- Quantum Thermodynamics
- Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
- Quantum heat engines and refrigerators: Continuous devices
- Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
- Work extraction and thermodynamics for individual quantum systems
- The resource theory of informational nonequilibrium in thermodynamics
- Entanglement entropy: holography and renormalization group
- Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping
- An introductory review of the resource theory approach to thermodynamics
- Entanglement Theory and the Second Law of Thermodynamics
- A Fresh Look at Entropy and the Second Law of Thermodynamics
- Phase Transitions in "Small" systems
- Quantum correlations and thermodynamic performances of two-qubit engines with local and collective baths
- Jarzynski Relations for Quantum Systems and Some Applications
- A reversible theory of entanglement and its relation to the second law
- Black holes and Boyle's law -- the thermodynamics of the cosmological constant
- Quantum work statistics close to equilibrium
- Stochastic independence as a resource in small-scale thermodynamics
- Stationary Motion of the Adiabatic Piston
- Axiomatic relation between thermodynamic and information-theoretic entropies
- Quantum thermodynamics of correlated-catalytic state conversion at small-scale
- A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium
- Resource convertibility and ordered commutative monoids
- The entropy concept for non-equilibrium states
- Universal Bounds on Fluctuations in Continuous Thermal Machines
- No second law of entanglement manipulation after all
- Quantization of Contact Manifolds and Thermodynamics
- Fundamental work cost of quantum processes
- From the adiabatic piston to macroscopic motion induced by fluctuations
- On the adiabatic properties of a stochastic adiabatic wall: Evolution, stationary non-equilibrium, and equilibrium states
- Optimal Efficiency of Heat Engines with Finite-Size Heat Baths
- Topological Heat Transport and Symmetry-Protected Boson Currents
- Notes on the Third Law of Thermodynamics.I
- Local Temperatures Out of Equilibrium
- Entropy and reversible catalysis
- Thermodynamic entropy as a Noether invariant
- The Gibbs "volume" entropy is incorrect
- Uniqueness and characterization theorems for generalized entropies
- The fourth law of thermodynamics: steepest entropy ascent
- Fundamental limitations on photoisomerization from thermodynamic resource theories
- Reviving quark nuggets as a candidate for dark matter
- Jarzynski equality for the transitions between nonequilibrium steady states
- The compressibility of rotating black holes in D-dimensions
- Operational definition of the temperature of a quantum state
- Bounds on fluctuations for finite-time quantum Otto cycle
- The law of entropy increase and the Meissner effect
- Recent Progress in the Definition of Thermodynamic Entropy
- Work Cost of Thermal Operations in Quantum and Nano Thermodynamics
- The first law of general quantum resource theories
- Thermodynamic Signatures of Genuinely Multipartite Entanglement
- Extracting work from quantum systems
- Thermodynamics from relative entropy
- Universal behaviour of ideal and interacting quantum gases in two dimensions
- Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston
- Resource theory of quantum uncomplexity
- Surpassing the Carnot Efficiency by extracting imperfect work
- Quantum Mutual Information Along Unitary Orbits
- A New Thermodynamics from Nuclei to Stars III
- Independence of work and entropy for equal energetic finite quantum systems: Passive state energy as an entanglement quantifier
- Regional Seismic Information Entropy for Detecting Precursors of Earthquake Activation
- A Resource Theory of Quantum Measurements
- Monotones in General Resource Theories
- Possible extended forms of thermodynamic entropy
- Shear transport far from equilibrium via holography
- The Thermodynamical Arrow of Time: Reinterpreting the Boltzmann-Schuetz Argument
- Intrinsic and extrinsic thermodynamics for stochastic population processes with multi-level large-deviation structure
- Reversibility of quantum resources through probabilistic protocols
- Reversing the Arrow of Time
- Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems
- Entropy Meters and the Entropy of Non-extensive Systems
- Quantum entanglement in the anisotropic Heisenberg model with multicomponent DM and KSEA interactions
- Quantum statistical mechanical derivation of the second law of thermodynamics: a hybrid setting approach
- Non-Markovian dynamics under time-translation symmetry
- Tsallis entropy induced metrics and CAT(k) spaces
- The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution in external potentials, N-dependence and the role of chaos
- Schwinger's Picture of Quantum Mechanics IV: Composition and independence
- On reduction of the wave-packet, decoherence, irreversibility and the second law of thermodynamics
- Characterizing symmetry-protected thermal equilibrium by work extraction
- Fully quantum second-law--like statements from the theory of statistical comparisons
- Study of bounds on non-equilibrium fluctuations for asymmetrically driven quantum Otto engine
- Classical and Quantum Mechanics via Lie algebras
- Thermodynamic constraints on fluctuation phenomena
- Order-preserving dynamics in one dimension -- single-file diffusion and caging from the perspective of dynamical density functional theory
- Primacy & Ranking of UEFA Soccer Teams from Biasing Organizing Rules
- Universal Property of Quantum Gravity implied by Uniqueness Theorem of Bekenstein-Hawking Entropy
- Experimental Validation of Enhanced Information Capacity by Quantum Switch in Accordance with Thermodynamic Laws
- -Generalized representation of the -dimensional Dirac delta and -Fourier transform
- The Physical Basis of the Gibbs-von Neumann entropy
- On the Second Law of thermodynamics and the piston problem
- Schrödinger's problem with cats: measurements and states in the Groupoid Picture of Quantum Mechanics
- Fermi's golden rule and the second law of thermodynamics
- The definition of the thermodynamic entropy in statistical mechanics
- Non-extensive Hamiltonian systems follow Boltzmann's principle not Tsallis statistics. -- Phase Transitions, Second Law of Thermodynamics
- On Black Hole Thermodynamics, Singularity, and Gravitational Entropy
- Global existence analysis of energy-reaction-diffusion systems
- Emergence of a second law of thermodynamics in isolated quantum systems
- Geometry induced local thermal current from cold to hot in a classical harmonic system
- Critique of the Gibbs volume entropy and its implication
- Information-theoretic foundations of thermodynamics in general probabilistic theories
- Landauer's principle as a special case of Galois connection
- The classification of preordered spaces in terms of monotones: complexity and optimization
- Emergence of Constructor-based Irreversibility in Quantum Systems: Theory and Experiment
- Axiomatic Information Thermodynamics
- Effect of quantum resonances on local temperature in nonequilibrium open systems
- Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma
- Second Law of Entanglement Manipulation with Entanglement Battery
- Quantum-phase-field concept of matter: Emergent gravity in the dynamic universe
- Compact convex structure of measurements and its applications to simulability, incompatibility, and convex resource theory of continuous-outcome measurements
- Accessibility of physical states and non-uniqueness of entanglement measure
- Emergence of a thermal equilibrium in a subsystem of a pure ground state by quantum entanglement
- Mesoscopic description of the adiabatic piston: kinetic equations and -theorem
- Data-Driven Inference, Reconstruction, and Observational Completeness of Quantum Devices
- Inevitability of knowing less than nothing
- Entropy and entanglement in polymer quantization
- Representing preorders with injective monotones
- Reverse Data-Processing Theorems and Computational Second Laws
- Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions
- Distributed Encoding and Decoding of Quantum Information over Networks
- One dimensional Brownian motion in hard rods: adiabatic piston problem
- Seeking Maxwell's Demon in a non-reciprocal quantum ring
- Belief in thermodynamics has provoked false thermodynamics of superconductors
- Quantum refrigeration powered by noise in a superconducting circuit
- Computable lower bounds on the entanglement cost of quantum channels
- Thermodynamics of structure-forming systems
- Smooth entropy in axiomatic thermodynamics
- A Scaling Approach to Ideal Quantum Gases
- Asymptotic quantification of entanglement with a single copy
- A definition of thermodynamic entropy valid for non-equilibrium states and few-particle systems
- Operational derivation of Maxwell-Boltzmann distribution with Maxwell's demon model
- Quantum harvester enables energy transfer without randomness transfer or dissipation
- Thermodynamic fluctuation theorems govern human sensorimotor learning
- Holographic pressure and volume for black holes
- Quantifying the value of transient voltage sources
- Straight way to Thermo-Statistics, Phase Transitions, Second Law of Thermodynamics, but without Thermodynamic Limit
- Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
- Steady state thermodynamics
- Single-shot work extraction in quantum thermodynamics revisited
- Relativism versus statistics in the microscopic foundation of thermodynamics
- Is the statement of Murphy's Law valid?
- Dynamical Gibbs Variational Principles for Irreversible Interacting Particle Systems with Applications to Attractor Properties
- Quark contribution for center domain in heavy ion collisions
- The Entropy Law and the impossibility of perpetual economic growth
- Quantum Information Measures in Quartic and Symmetric Potentials using perturbative approach
- Temperature as Joules per Bit
- Active electron cooling of graphene
- Inevitable Negativity: Additivity Commands Negative Quantum Channel Entropy
- Thermodynamics for Trajectories of a Mass Point
- Entanglement, loss, and quantumness: When balanced beam splitters are best
- Assessing thermalization and estimating the Hamiltonian with output data only
- Testing the Quantum of Entropy
- Towards the microscopic foundation of the zeroth law of thermodynamics
- On the foundations of thermodynamics
- What Have Spacetime, Shape and Symmetry to Do with Thermodynamics?
- Majorization requires infinitely many second laws
- Categories of Brègman operations and epistemic (co)monads
- Ambiguities in order-theoretic formulations of thermodynamics
- Multidimensional arrow of time
- Relativistic kinetic theory of classical systems of charged particles: towards the microscopic foundation of thermodynamics and kinetics
- Entropy in Themodynamics: from Foliation to Categorization
- Work done on a single-particle gas during an adiabatic compression/expansion process
- Thermodynamics approach to near future of civilization
- Quantum Tomography and Schwinger's Picture of Quantum Mechanics
- Statistical ensembles for phase coexistence states specified by noncommutative additive observables
- Work as a Memory Record
- Thermodynamics of bipartite entanglement
- Thermodynamics and phase transitions of black holes in contact with a gravitating heat bath
- Time and its arrow: an empiricist's perspective
- Entropy production for quasi-adiabatic parameter changes dominated by hydrodynamics
- Existence and order of the phase transition of the Ising model with fixed magnetization
- Countability constraints in order-theoretic approaches to computability
- Spontaneous breakdown of the time reversal symmetry
- Bluff your way in the second law of thermodynamics
- On Thermodynamic Interpretation of Copula Entropy
- Universal Property of Quantum Gravity implied by Bekenstein-Hawking Entropy and Boltzmann formula
- Self similarity of the expanding universe as understood by quantum-phase-fields
- Infinite dimensionality of the post-processing order of measurements on a general state space
- Becoming Large, Becoming Infinite: The Anatomy of Thermal Physics and Phase Transitions in Finite Systems
- Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
- From the 2nd Law of Thermodynamics to AC-Conductivity Measures of Interacting Fermions in Disordered Media
- On the use of non-canonical quantum statistics
- Deep learning of thermodynamic laws from microscopic dynamics
- The second law of thermodynamics from concave energy in classical mechanics
- Entropy: An inherent, nonstatistical property of any system in any state
- On the explanation for quantum statistics
- Thermodynamic properties and Hilbert space of the human brain