A Dynamical Systems Theory of Thermodynamics
Wassim M. Haddad
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A brand-new conceptual look at dynamical thermodynamics
This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics.
This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics.
A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.
Quantum fluctuation, Thermodynamic process, Einstein relation (kinetic theory), State-space representation, Fermion, Chemical kinetics, Statistical physics, Temperature, Entropy production, Gravitational field, Lorentz covariance, Harmonic oscillator, Zeroth law of thermodynamics, Internal energy, Cosmological constant, Balance equation, Gas laws, Moduli (physics), Thermodynamic state, Classical mechanics, Laws of thermodynamics, Second law of thermodynamics, Newton's law of universal gravitation, Relativistic mechanics, Superfluidity, Diathermal wall, Special relativity, Thermodynamic equilibrium, Non-equilibrium thermodynamics, Statistical mechanics, Monatomic gas, Geodesics in general relativity, Relativistic dynamics, Theory of heat, Stress–energy tensor, Scalar (physics), Equilibrium thermodynamics, Law of mass action, Einstein tensor, First law of thermodynamics, Electroweak interaction, Lorentz transformation, Quantum mechanics, Conservation of energy, Thermodynamic system, Available energy (particle collision), Third law of thermodynamics, Electrochemical potential, Thermal equilibrium, Thermohaline circulation, Hamiltonian mechanics, Equipartition theorem, Boltzmann's entropy formula, Dynamical system, Heat transfer, Microstate (statistical mechanics), Chemical thermodynamics, Theoretical physics, Degrees of freedom (mechanics), Diffusion equation, Carnot's theorem (thermodynamics), Gauge theory, Photon, Subatomic particle, Kinetic theory of gases, Thermodynamic temperature, Langevin equation, Reversible process (thermodynamics), Stability theory, Fermi–Dirac statistics, Boltzmann constant, Mass–energy equivalence, Energy–momentum relation, Fluctuation theorem, Einstein field equations, Black hole thermodynamics, Newton's law of cooling, Chemical potential, Gravitational potential, Relativistic Doppler effect, Gravitational constant, Thermodynamics, Stochastic differential equation, Theory of relativity, Bose–Einstein statistics