Contact Hamiltonian Mechanics

Abstract

In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.

40 pages, final version accepted in Annals of Physics

References in corpus (11)

• Quantum critical scaling of the geometric tensors
• A Hamilton-Jacobi Formalism for Thermodynamics
• Quantization of Contact Manifolds and Thermodynamics
• Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian
• A thermostat algorithm generating target ensembles
• Liouville's Theorem and the canonical measure for nonconservative systems from contact geometry
• Contact geometric descriptions of vector fields on dually flat spaces and their applications in electric circuit models and nonequilibrium statistical mechanics
• The principle of stationary nonconservative action for classical mechanics and field theories
• Time-evolution of quantum systems via a complex nonlinear Riccati equation II. Dissipative systems
• Geometric integrator for simulations in the canonical ensemble
• Geometry and structure of quantum phase space

Cited by in corpus (73)

• Thermodynamic geometry for charged Gauss-Bonnet black holes in AdS spacetimes
• Cosymplectic and contact structures to resolve time-dependent and dissipative hamiltonian systems
• Imperfect fluid description of modified gravities
• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
• Contact manifolds and dissipation, classical and quantum
• A contact geometry framework for field theories with dissipation
• Contact variational integrators
• Contact geometry and thermodynamics of black holes in AdS spacetimes
• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
• Dynamical Similarity
• A $k$-contact Lagrangian formulation for nonconservative field theories
• A novel approach to contact Hamiltonians and contact Hamilton-Jacobi theory
• Cosmological perturbations for two cold fluids in $\Lambda$CDM
• Vanishing contact structure problem and convergence of the viscosity solutions
• A New Action for Cosmology
• Scalar Fields and the FLRW Singularity
• On the role of geometry in statistical mechanics and thermodynamics I: Geometric perspective
• When scale is surplus
• Multicontact formulation for non-conservative field theories
• Numerical integration in celestial mechanics: a case for contact geometry
• A framework of nonequilibrium statistical mechanics. I. Role and type of fluctuations
• On the lagrangian description of dissipative systems
• Unified Lagrangian-Hamiltonian formalism for contact systems
• Symmetries, conservation and dissipation in time-dependent contact systems
• Convergence of viscosity solutions of generalized contact Hamilton-Jacobi equations
• Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Extended Hamilton-Jacobi theory, contact manifolds and integrability by quadratures
• Geometrical Formulation of Relativistic Mechanics
• Higher-order contact mechanics
• Reductions: precontact versus presymplectic
• Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras
• Nonautonomous k-contact field theories
• Contact Lie systems
• Contact Lagrangian systems subject to impulsive constraints
• Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds
• The Herglotz variational principle for dissipative field theories
• Exact Baker-Campbell-Hausdorff formula for the contact Heisenberg algebra
• Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems
• Global dynamics of contact Hamiltonian systems (I): monotone systems
• Contactifications: a Lagrangian description of compact Hamiltonian systems
• Generalized virial theorem for contact Hamiltonian systems
• Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle
• Nonequilibrium thermodynamic process with hysteresis and metastable states -- A contact Hamiltonian with unstable and stable segments of a Legendre submanifold
• Multidimensional integrable systems from contact geometry
• Perturbation-theory informed integrators for cosmological simulations
• Practical Introduction to Action-Dependent Field Theories
• Light propagation through optical media using metric contact geometry
• Herglotz' variational principle and Lax-Oleinik evolution
• Starting Cosmological Simulations from the Big Bang
• The flow method for the Baker-Campbell-Hausdorff formula: exact results
• Contact geometry and quantum thermodynamics of nanoscale steady states
• Lagrangian description of Heisenberg and Landau-von Neumann equations of motion
• Formulation of Stochastic Contact Hamiltonian Systems
• Sasaki-Ricci flow equation on five-dimensional Sasaki-Einstein space $Y^{p,q}$
• Invariant measures for some dissipative systems from the Jacobi last multiplier
• Hamilton-Jacobi approach to thermodynamic transformations
• Contact Lie systems on Riemannian and Lorentzian spaces: from scaling symmetries to curvature-dependent reductions
• Fast symplectic integrator for Nesterov-type acceleration method
• Contact Dynamics versus Legendrian and Lagrangian Submanifolds
• Contact Hamiltonian dynamics and perturbed contact instantons with Legendrian boundary condition
• Skinner-Rusk formalism for k-contact systems
• Constrained Lagrangian dissipative contact dynamics
• When action is not least for systems with action-dependent Lagrangians
• Equilibria and bifurcations in contact dynamics
• New directions for contact integrators
• On Geometrical Couplings of Dissipation and Curl Forces
• Hessian-information geometric formulation of Hamiltonian systems and generalized Toda's dual transform
• Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimization
• Information and contact geometric description of expectation variables exactly derived from master equations
• Generalized action-angle coordinates in toric contact spaces
• Geometric numerical integration of Liénard systems via a contact Hamiltonian approach
• Exponential convergence of 1-graph of the solution semigroup of contact Hamilton-Jacobi equations