Thermodynamic laws in isolated systems

Abstract

The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying microcanonical thermostatistics. Here, we provide a detailed comparison of the most commonly considered microcanonical entropy definitions, focussing specifically on whether they satisfy or violate the zeroth, first and second law of thermodynamics. Our analysis shows that, for a broad class of systems that includes all standard classical Hamiltonian systems, only the Gibbs volume entropy fulfills all three laws simultaneously. To avoid ambiguities, the discussion is restricted to exact results and analytically tractable examples.

footnotes 19, 26 and outlook section added

References in corpus (25)

• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential
• Negative Absolute Temperature for Motional Degrees of Freedom
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Universal features in the energetics of symmetry breaking
• Inconsistent thermostatistics and negative absolute temperatures
• Nonequilibrium work distribution of a quantum harmonic oscillator
• Classification of phase transitions in small systems
• Microcanonical Analyses of Peptide Aggregation Processes
• Phase Transitions in Small Systems: Microcanonical vs. Canonical Ensembles
• Fluctuation and dissipation of work in a Joule experiment
• Heat-machine control by quantum-state preparation: from quantum engines to refrigerators
• Equilibration rates and negative absolute temperatures for ultracold atoms in optical lattices
• Microcanonical quantum fluctuation theorems
• Microcanonical mean-field thermodynamics of self-gravitating and rotating systems
• Thermodynamics of Peptide Aggregation Processes. An Analysis from Perspectives of Three Statistical Ensembles
• System-size scaling of Boltzmann and alternate Gibbs entropies
• Statistics of work and fluctuation theorems for microcanonical initial states
• Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation
• Finite Bath Fluctuation Theorem
• Inexistence of equilibrium states at absolute negative temperatures
• Logarithmic oscillators: ideal Hamiltonian thermostats
• The Origins of Phase Transitions in Small Systems
• Thermodynamics with generalized ensembles: The class of dual orthodes
• Thermostated Hamiltonian dynamics with log-oscillators

Cited by in corpus (43)

• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
• Efficiency of a quantum Otto heat engine operating under a reservoir at effective negative temperatures
• Statistical Mechanics of Systems with Negative Temperature
• Consistent description of fluctuations requires negative temperatures
• On the dispute between Boltzmann and Gibbs entropy
• Negative temperatures and the definition of entropy
• Fermi's golden rule for spontaneous emission in absorptive and amplifying media
• Meaning of temperature in different thermostatistical ensembles
• The Gibbs "volume" entropy is incorrect
• Canonical free-energy barrier of particle and polymer cluster formation
• Operational definition of the temperature of a quantum state
• Quantum Otto cycle efficiency on coupled qudits
• In defence of negative temperature
• Phase transitions at high energy vindicate negative microcanonical temperature
• Typical and extreme entropies of long-lived isolated quantum systems
• Quantized quasinormal mode theory of coupled lossy and amplifying resonators
• Relation between Boltzmann and Gibbs entropy and example with multinomial distribution
• The thermodynamic entropy of a macroscopic quantum system is a continuous function of energy
• Cosmology with Negative Absolute Temperatures
• The Mereology of Thermodynamic Equilibrium
• Equilibration of energy in slow-fast systems
• Entropy and Temperature in finite isolated quantum systems
• Origin of Negative Temperatures in Systems Interacting with External Fields
• Microcanonical entropy for classical systems
• Entropy and the second law for driven, or quenched, thermally isolated systems
• The stumbling block of the Gibbs entropy: the reality of the negative absolute temperatures
• Strong Coupling and non-Markovian Effects in the Statistical Notion of Temperature
• Quantifying Information Extraction using Generalized Quantum Measurements
• Negative temperature is cool for cooling
• Feasible platform to study negative temperatures
• Canonical density matrices from eigenstates of mixed systems
• Non-Clausius heat transfer: the example of harmonic chain with an impurity
• A microcanonical entropy correcting finite-size effects in small systems
• Increase of quantum volume entropy in presence of degenerate eigenenergies
• Exponential energy growth due to slow parameter oscillations in quantum mechanical systems
• How Geometrical Frustrated Systems Challenge our Notion of Thermodynamics
• Resolving the debate about proposed expressions for the classical entropy
• Quasistatic work processes: When slowness implies certainty
• Verification of finite bath fluctuation theorem for a non-ergodic system
• Coarse-graining and symplectic non-squeezing
• Ensemble equivalence for mean field models and plurisubharmonicity
• Thermodynamics of fluctuations in small systems interacting with the environment
• The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies