| entropy | |
|---|---|
| Name | Entropy |
| Symbols | S, H, S_vN |
| Unit | k_B (J·K^−1) |
| Dimension | state variable |
entropy
Entropy in quantum physics quantifies the amount of missing information, disorder, or microscopic uncertainty associated with a quantum state and underpins the link between quantum mechanics and thermodynamics. It matters for understanding thermalization, decoherence, the limits of quantum computing, and the ethical distribution of technological benefits in a society facing climate and inequality challenges.
In quantum systems, entropy generalizes classical notions of disorder to account for superposition and noncommuting observables. For a system described by a density operator ρ on a Hilbert space, entropy measures the lack of knowledge about pure state vectors and the multiplicity of microstates compatible with macroscopic constraints. This quantum perspective is central to work at institutions such as CERN, MIT, and Perimeter Institute where foundations of quantum field theory and many-body physics intersect with statistical concepts. Quantum entropy connects to operational tasks in quantum information theory and to early theoretical contributions by Ludwig Boltzmann, Josiah Willard Gibbs, and John von Neumann.
The standard measure is the von Neumann entropy, S(ρ) = −Tr(ρ log ρ), introduced by John von Neumann in correspondence with Shannon's work. von Neumann entropy quantifies information content in protocols developed at places like Bell Labs and analyzed by researchers such as Claude Shannon and Leonard J. Schulman. It underlies limits in quantum communication (e.g., Holevo's theorem), the capacity of quantum channels, and resource theories studied at University of Cambridge and Caltech. Related named measures include Rényi entropy and Tsallis entropy, which appear in theoretical studies and experimental tests by groups at IBM Quantum and Google Quantum AI.
Entropy growth tracks the loss of coherence when a quantum system interacts with an environment. The process of decoherence—developed by theorists like Wojciech Zurek—explains emergence of classicality as entanglement with an environment increases von Neumann entropy of subsystems. In open quantum systems described by Lindblad equation dynamics, entropy production quantifies irreversibility; similar concepts are tested in cold-atom platforms at Max Planck Institute for Quantum Optics and Harvard University. Thermalization in isolated many-body systems invokes the eigenstate thermalization hypothesis (ETH), studied numerically by groups at Los Alamos National Laboratory and in experiments at Joint Quantum Institute.
Entanglement entropy—entropy of reduced density matrices—measures quantum correlations between subsystems and has become a central diagnostic in condensed matter physics, quantum gravity, and quantum field theory. The area law for entanglement entropy relates entropy to boundary geometry, connecting to insights from AdS/CFT correspondence and work by Juan Maldacena. Entanglement entropy is used in tensor network methods like matrix product states and MERA developed by researchers at Perimeter Institute and University of Vienna to study many-body phases. Experimentally, entanglement measures are probed in systems by teams at NIST, Oxford University, and ETH Zurich.
Quantum entropy underpins the definition of ensembles—microcanonical, canonical, and grand canonical—in quantum statistical mechanics following the foundations laid by Gibbs and Boltzmann. The second law of thermodynamics is formulated in quantum settings via monotonicity of relative entropy (the Uhlmann theorem and Lieb–Ruskai theorem), with mathematical work by Elliott Lieb and Mary Beth Ruskai. Quantum versions of the Carnot cycle and fluctuation theorems (e.g., work of Christopher Jarzynski and Gavin Crooks) connect microscopic entropy changes to macroscopic heat engines. Laboratories at Los Alamos National Laboratory and companies like D-Wave Systems explore thermodynamic behavior in engineered quantum devices.
Entropy production quantifies irreversible processes in quantum dynamics, with formalizations via quantum stochastic thermodynamics and the study of nonequilibrium steady states. Research groups at École Normale Supérieure and University of Tokyo study entropy flows, quantum fluctuation relations, and resource-theoretic bounds. There are justice implications: energy costs of quantum technologies, environmental impacts of large computing facilities, and unequal access to quantum advancements raise ethical questions addressed by scholars at Harvard Kennedy School and advocacy organizations focused on equitable science policy. Transparent accounting of entropy and thermodynamic costs can inform fair technology deployment and climate justice strategies.
Entropy constraints set bounds on error correction, cooling requirements, and computational complexity in quantum computing architectures developed by IBM, Google, and academic consortia. Quantum error correction codes (e.g., surface code) rely on entropy management to protect logical qubits; researchers at Microsoft Research study thermodynamic costs of fault tolerance. Quantum thermodynamics explores nanoscale engines and refrigerators with experimental groups at University of Basel and Technical University of Munich. Societal impacts include potential reductions in energy use for certain computations, but also the carbon footprint of quantum infrastructure; policy discussions involving United Nations agencies, national laboratories, and civil society emphasize equitable access, responsible innovation, and aligning breakthroughs with public benefit.
Category:Quantum physics Category:Thermodynamics Category:Quantum information theory