Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. IV: Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics

Abstract

This is the fourth paper, the last one, on solution to the problem of absence of detailed balance in nonequilibrium processes. It is an approach based on another known universal dynamics: The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology; The statistical mechanics and thermodynamics, while enormously successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding; Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach: One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.

latex, 49 pages

References in corpus (20)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Steady State Thermodynamics of Langevin Systems
• Canonical Typicality
• The Nonequilibrium Thermodynamics of Small Systems
• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. II: construction of SDS with nonlinear force and multiplicative noise
• Statistical Mechanics: A Selective Review of Two Central Issues
• A new calculation of the mass fraction of primordial black holes
• The Einstein relation generalized to non-equilibrium
• Structure of Stochastic Dynamics near Fixed Points
• Dynamics of Shear-Transformation Zones in Amorphous Plasticity: Formulation in Terms of an Effective Disorder Temperature
• Laws in Darwinian Evolutionary Theory
• Calculating Biological Behaviors of Epigenetic States in Phage lambda Life Cycle
• Non-equilibrium work relations
• The unreasonable effectiveness of equilibrium-like theory for interpreting non-equilibrium experiments
• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. III: potential function in local stochastic dynamics and in steady state of Boltzmann-Gibbs type distribution function
• Nonequilibrium Approach to Bloch-Peierls-Berry Dynamics
• Nonequilibrium Potential Function of Chemically Driven Single Macromolecules via Jarzynski-Type Log-Mean-Exponential Work
• Efficiency, Robustness and Stochasticity of Gene Regulatory Networks in Systems Biology: lambda Switch as a Working Example

Cited by in corpus (50)

• Nonequilibrium Physics in Biology
• The Physical Origins of Entropy Production, Free Energy Dissipation and their Mathematical Representations
• Path integrals, particular kinds, and strange things
• Social cycling and conditional responses in the Rock-Paper-Scissors game
• Stochastic approach to equilibrium and nonequilibrium thermodynamics
• The contribution of statistical physics to evolutionary biology
• Thermodynamic Limit of a Nonequilibrium Steady-State: Maxwell-Type Construction for a Bistable Biochemical System
• Noise-induced drift in stochastic differential equations with arbitrary friction and diffusion in the Smoluchowski-Kramers limit
• Some interesting observations on the free energy principle
• Beyond Itô versus Stratonovich
• A Decomposition of Irreversible Diffusion Processes Without Detailed Balance
• Stochastic thermodynamics for delayed Langevin systems
• Non-equilibrium fluctuations for linear diffusion dynamics
• A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales
• Constructive Proof of Global Lyapunov Function as Potential Function
• Relation of a New Interpretation of Stochastic Differential Equations to Ito Process
• Exact Mapping Noisy van der Pol Type Oscillator onto Quasi-symplectic Dynamics
• Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics
• Determine dynamical behaviors by the Lyapunov function in competitive Lotka-Volterra systems
• Nonequilibrium Steady State Driven by a Nonlinear Drift Force
• A variational synthesis of evolutionary and developmental dynamics
• Summing over trajectories of stochastic dynamics with multiplicative noise
• Towards physical principles of biological evolution
• The Zeroth Law of Thermodynamics and Volume-Preserving Conservative Dynamics with Equilibrium Stochastic Damping
• Analytical Mechanics in Stochastic Dynamics: Most Probable Path, Large-Deviation Rate Function and Hamilton-Jacobi Equation
• Stochastic Physics, Complex Systems and Biology
• Boltzmann-Gibbs entropy is sufficient but not necessary for the likelihood factorization required by Einstein
• Work Relations Connecting Nonequilibrium Steady States Without Detailed Balance
• A generalized integral fluctuation theorem for diffusion processes
• Non-equilibrium work relation beyond Boltzmann-Gibbs distribution
• Kinematic Basis of Emergent Energetics of Complex Dynamics
• Fitness and entropy production in a cell population dynamics with epigenetic phenotype switching
• Is the free-energy principle a formal theory of semantics? From variational density dynamics to neural and phenotypic representations
• Statistical Genetics in and out of Quasi-Linkage Equilibrium (Extended)
• Topology, Vorticity and Limit Cycle in a Stabilized Kuramoto-Sivashinsky Equation
• Sex as Gibbs Sampling: a probability model of evolution
• From chemical Langevin equations to Fokker-Planck equation: application of Hodge decomposition and Klein-Kramers equation
• Fluctuation-dissipation relations far from equilibrium
• Comment on "On Uniqueness of SDE Decomposition in A-type Stochastic Integration" [arXiv:1603.07927v1]
• Shifting gears: Thermodynamics of genetic information storage suggest stress-dependence of mutation rate, which can accelerate adaptation
• Small Open Chemical Systems Theory and Its Implications to Darwinian Evolutionary Dynamics, Complex Self-Organization and Beyond
• Statistical physics of flux-carrying Brownian particles
• SVD-based Causal Emergence for Gaussian Iterative Systems
• Multi-AI competing and winning against humans in iterated Rock-Paper-Scissors game
• Kinetics of Muller's Ratchet from Adaptive Landscape Viewpoint
• Global View of Bionetwork Dynamics: Adaptive Landscape
• Landscape construction in non-gradient dynamics: A case from evolution
• Defining and finding lifelike entities with a lazy filter
• A Hamiltonian-Entropy Production Connection in the Skew-symmetric Part of a Stochastic Dynamics
• Flow Decomposition Reveals Dynamical Structure of Markov Process