arXiv subjects

Mingnan Ding

Publications and source records attributed to Mingnan Ding.

18 recordsLinked to original sources

arXiv2026

Microscopic Dynamical Entropy I: Quantifying Hamiltonian Irreversibility in Large and Small Systems

We introduce a Microscopic Dynamical Entropy (MDE) for Hamiltonian systems, defined with respect to a chosen partition of degrees of freedom into a system X and its environment Y. The construction is based on the conditional phase-space volume (CPV), or conditional Boltzmann entropy, associated with the unmonitored degrees of freedom Y. The MDE is a microscopically defined entropy functional of the marginal distribution $\rho_X(t)$, obtained by discarding conditional microscopic information associated with Y from the Gibbs entropy of the joint XY system, while retaining exact Hamiltonian dynamics. This construction clarifies the microscopic origin of thermal entropy. The dependence of MDE solely on $\rho_X(t)$ is consistent with the thermodynamic assumption that the entropy increment of a heat bath Y depends on its heat content and temperature, not on details of its probability distribution. Indeed, the MDE recovers dS = dQ/T connecting entropy increments to heat flow between system and environment. More generally, it provides a consistent description of irreversible relaxation under exact Hamiltonian dynamics, while permitting transient entropy decreases in small systems and in spin-echo type protocols. Under time-scale separation between X and Y, the MDE becomes strictly monotonic in time, recovering the familiar structure of irreversible thermodynamics. The MDE can foreshadow thermodynamics even in a small isolated Hamiltonian system, if X is a well chosen subset of its degrees of freedom. An example is the centre of mass of interacting particles confined to a box. Even for as few as N=10 particles, the MDE increases during relaxation towards a maximum at equilibrium, with increasing monotonicity at larger N. Taken together, our results show that the MDE offers a microscopic interpretation of nonequilibrium thermal entropy and its time dependence within exact Hamiltonian dynamics.

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arXiv2026

Microscopic Dynamical Entropy II: Statistical and Stochastic Thermodynamics of Hamiltonian Systems

The Microscopic Dynamical Entropy (MDE) introduced in Ref. [1] describes irreversible relaxation of selected variables x within a finite closed Hamiltonian system of fixed total energy E. Here we extend the framework to arbitrary total-energy distributions and time-dependent Hamiltonians. This allows work interactions with external agents or protocols, crucial in stochastic and classical thermodynamics, and driven systems more generally, to be addressed directly. The central step is to reduce the full microscopic description in terms of selected variables x and unmonitored variables y to one in terms of the selected variables and the instantaneous total energy (x,E). The unmonitored degrees of freedom y in Y enter through their conditional phase-space volume (CPV) $\Omega_Y(x,E,t)$. This construction allows work and heat to be defined directly for finite Hamiltonian composites, including cases where Y is so small that its temperature is not well defined. We demonstrate monotonic MDE growth, corresponding to the macroscopic second law, under mixing and time-scale separation even for driven systems with arbitrary energy distributions. At trajectory level, we derive detailed and integral fluctuation relations for the MDE, generalising standard large-bath results. We verify these numerically in a driven few-particle Hamiltonian system, showing the emergence of stochastic thermodynamics for collective coordinates, such as the centre-of-mass position, even in closed systems with only ten or twenty degrees of freedom. Physically, these fluctuation relations connect irreversibility to the change in the number of unmonitored microstates compatible with initial and final data for the observed coordinates. Together, our results provide a finite-system Hamiltonian foundation for the emergence of classical and stochastic thermodynamics and extend their applicability to surprisingly small heat baths.

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arXiv2025

Hamiltonian Heat Baths, Coarse-Graining and Irreversibility: A Microscopic Dynamical Entropy from Classical Mechanics

The Hamiltonian evolution of an isolated classical system is reversible, yet the second law of thermodynamics states that its entropy can only increase. This has confounded attempts to identify a `Microscopic Dynamical Entropy' (MDE), by which we mean an entropy computable from the system's evolving phase-space density $\rho(t)$, that equates {\em quantitatively} to its thermodynamic entropy $S^{\rm th}(t)$, both within and beyond equilibrium. Specifically, under Hamiltonian dynamics the Gibbs entropy of $\rho$ is conserved in time; those of coarse-grained approximants to $\rho$ show a second law but remain quantitatively unrelated to heat flow. Moreover coarse-graining generally destroys the Hamiltonian evolution, giving paradoxical predictions when $\rho(t)$ exactly rewinds, as it does after velocity-reversal. Here we derive the MDE for an isolated system XY in which subsystem Y acts as a heat bath for subsystem X. We allow $\rho_{XY}(t)$ to evolve without coarse-graining, but compute its entropy by disregarding the detailed structure of $\rho_{Y|X}$. The Gibbs entropy of the resulting phase-space density $\tilde\rho_{XY}(t)$ comprises the MDE for the purposes of both classical and stochastic thermodynamics. The MDE obeys the second law whenever $\rho_X$ evolves independently of the details of Y, yet correctly rewinds after velocity-reversal of the full XY system.

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arXiv2025

An ideal entropy transporter with finite power and vanishing fluctuation

We study a micro-magnet that interacts with a spin-polarized electric current, a heat bath, as well as a static magnetic field. The resulting non-equilibrium steady-state transports entropy between the current and the heat bath, without need of any thermodynamic force. In the limit of strong magnetic field, both the entropy production rate and the fluctuation of entropy transport become vanishingly small, whereas the average rate of entropy transport remains finite. Our results demonstrate that there is no fundamental limitation on the performance of thermodynamic engines other than the first and second laws of thermodynamics.

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arXiv2024

Stochastic Thermodynamics of Micromagnetics with Spin Torque

In this work, we study the stochastic dynamics of micro-magnetics interacting with a spin-current torque. We extend the previously constructed stochastic Landau-Lifshitz equation to the case with spin-current torque, and verify the conditions of detailed balance. Then we construct various thermodynamics quantities such as work and heat, and prove the second law of thermodynamics. Due to the existence of spin-torque and the asymmetry of the kinetic matrix, a novel effect of entropy pumping shows up. As a consequence, the system may behave as a heat engine which constantly transforms heat into magnetic work. Finally, we derive a fluctuation theorem for the joint probability density function of the pumped entropy and the total work, and verify it using numerical simulations.

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arXiv2024

Stochastic thermodynamics of Brownian motion in a flowing fluid

We study stochastic thermodynamics of over-damped Brownian motion in a flowing fluid. Unlike some previous works, we treat the effects of the flow field as a non-conservational driving force acting on the Brownian particle. This allows us to apply the theoretical formalism developed in a recent work for general non-conservative Langevin dynamics. We define heat and work both at the trajectory level and at the ensemble level, and prove the second law of thermodynamics explicitly. The entropy production (EP) is decomposed into a housekeeping part and an excess part, both of which are non-negative at the ensemble level. Fluctuation theorems are derived for the housekeeping work, the excess work, and the total work, which are further verified using numerical simulations. A comparison between our theory and an earlier theory by Speck et. al. is also carried out.

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arXiv2024

Stochastic Thermodynamics of Micromagnetics

In this work, we study the stochastic thermodynamics of micro-magnetic systems. We first formulate the stochastic dynamics of micro-magnetic systems by incorporating noises into Landau-Lifshitz (LL) equation, which describes the irreversible and deterministic dynamics of magnetic moments. The resulting stochastic Landau-Lifshitz (sLL) equation obeys detailed balance, which guarantees that, with the external field fixed, the system converges to thermodynamic equilibrium with vanishing entropy production and with non-vanishing probability current. We then discuss various thermodynamic variables both at the trajectory level and at the ensemble level, and further establish both the first and the second laws of thermodynamics. Finally, we establish fluctuation theorems, and verify them using numerical simulations.

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arXiv2023

Stochastic Thermodynamics of Brownian motion in Temperature Gradient

We study stochastic thermodynamics of a Brownian particle which is subjected to a temperature gradient and is confined by an external potential. We first formulate an over-damped Ito-Langevin theory in terms of local temperature, friction coefficient, and steady state distribution, all of which are experimentally measurable. We then study the associated stochastic thermodynamics theory. We analyze the excess entropy production (EP) both at trajectory level and at ensemble level, and derive the Clausius inequality as well as the transient fluctuation theorem (FT). We also use molecular dynamics to simulate a Brownian particle inside a Lennard-Jones fluid and verify the FT. Remarkably we find that the FT remains valid even in the under-damped regime. We explain the possible mechanism underlying this surprising result.

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arXiv2022

Covariant Non-equilibrium Thermodynamics from Ito-Langevin Dynamics

Using the recently developed covariant Ito-Langevin dynamics, we develop a non-equilibrium thermodynamic theory for small systems coupled to multiplicative noises. The theory is based on Ito-calculus, and is fully covariant under time-independent nonlinear transformation of variables. Assuming instantaneous detailed balance, we derive expressions for various thermodynamic functions, including work, heat, entropy production, and free energy, both at ensemble level and at trajectory level, and prove the second law of thermodynamics for arbitrary non-equilibrium processes. We relate time-reversal asymmetry of path probability to entropy production, and derive its consequences such as fluctuation theorem and non-equilibrium work relation. For Langevin systems with additive noises, our theory is equivalent to the common theories of stochastic energetics and stochastic thermodynamics. We also discuss examples of multiplicative noises where the common theories are inapplicable, but our theory yields correct results.

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arXiv2022

Evading Thermodynamic Uncertainty Relations via Asymmetric Dynamic Protocols

Many versions of Thermodynamic Uncertainty Relations (TUR) have recently been discovered, which impose lower bounds on relative fluctuations of integrated currents in irreversible dissipative processes, and suggest that there may be fundamental limitations on the precision of small scale machines and heat engines. In this work we rigorously demonstrate that TUR can be evaded by using dynamic protocols that are asymmetric under time-reversal. We illustrate our results using a model heat engine using two-level systems, and also discuss heuristically the fundamental connections between TUR and time-reversal symmetry.

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arXiv2022

Time-Slicing Path-integral in Curved Space

Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them covariant with respect to nonlinear transform of variables. In this work, we construct rigorous and covariant formulations of time-slicing path integrals for quantum and classical stochastic dynamics in curved space. We first establish a rigorous criterion for correct time-slice actions of path integrals (Lemma 1). This implies the existence of infinitely many equivalent representations for time-slicing path integral. We then show that, for any dynamics with second order generator, all time-slice actions are asymptotically equivalent to a Gaussian (Lemma 2). Using these results, we further construct a continuous family of equivalent actions parameterized by an interpolation parameter $α\in [0,1]$ (Lemma 3). The action generically contains a spurious drift term linear in $Δ\boldsymbol x$, whose concrete form depends on $α$. Finally we also establish the covariance of our path-integral formalism, by demonstrating how the action transforms under nonlinear transform of variables. The $α= 0$ representation of time-slice action is particularly convenient because it is Gaussian and invariant, as long as $Δ\boldsymbol x$ transforms according to Ito's formula.

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arXiv2021

Strong Coupling Thermodynamics and Stochastic Thermodynamics from the Unifying Perspective of Time-Scale Separation

Assuming time-scale separation, a simple and unified theory of thermodynamics and stochastic thermodynamics is constructed for small classical systems strongly interacting with its environment in a controllable fashion. The total Hamiltonian is decomposed into a bath part and a system part, the latter being the Hamiltonian of mean force. Both the conditional equilibrium of bath and the reduced equilibrium of the system are described by canonical ensemble theories with respect to their own Hamiltonians. The bath free energy is independent of the system variables and the control parameter. Furthermore, the weak coupling theory of stochastic thermodynamics becomes applicable almost verbatim, even if the interaction and correlation between the system and its environment are strong and varied externally. Finally, this TSS-based approach also leads to some new insights about the origin of the second law of thermodynamics.

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arXiv2020

Information Swimmer: A Novel Mechanism of Self-propulsion

We study an information-based mechanism of self-propulsion in noisy environment. An information swimmer maintains directional motion by periodically measuring its velocity and accordingly adjusting its friction coefficient. Assuming that the measurement and adjustment are reversible and hence cause no energy dissipation, an information swimmer may move without external energy input. There is however no violation of the second law of thermodynamics, because the information entropy stored in the memory of swimmer increases monotonically. By optimizing its control parameters, the swimmer can achieve a steady velocity that is comparable to the root-mean-square velocity of an analogous Brownian particle. We also define a swimming efficiency in terms of information entropy production rate, and find that in equilibrium media with white noises, information swimmers are generally less efficient than Brownian particles driven by constant forces. For colored noises with long correlation times, the frequency of measurement can be greatly reduced without affecting the efficiency of information swimmers.

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arXiv2020

Covariant Formulation of Non-linear Langevin Theory with Multiplicative Gaussian White Noises

The multi-dimensional non-linear Langevin equation with multiplicative Gaussian white noises in Ito's sense is made covariant with respect to non-linear transform of variables. The formalism involves no metric or affine connection, works for systems with or without detailed balance, and is substantially simpler than previous theories. Its relation with deterministic theory is clarified. The unitary limit and Hermitian limit of the theory are examined. Some implications on the choices of stochastic calculus are also discussed.

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arXiv2019

Action Principle and Dynamic Ensemble Theory for Non-equilibrium Markov Chains

An overarching action principle, the principle of minimal free action, exists for ergodic Markov chain dynamics. Using this principle and the Detailed Fluctuation Theorem, we construct a dynamic ensemble theory for non-equilibrium steady states (NESS) of Markov chains, which is in full analogy with equilibrium canonical ensemble theory. Concepts such as energy, free energy, Boltzmann macro-sates, entropy, and thermodynamic limit all have their dynamic counterparts. For reversible Markov chains, minimization of Boltzmann free action yields thermal equilibrium states, and hence provide a dynamic justification of the principle of minimal free energy. For irreversible Markov chains, minimization of Boltzmann free action selects the stable NESS, and determines its macroscopic properties, including entropy production. A quadratic approximation of free action leads to linear-response theory with reciprocal relations built-in. Hence, in so much as non-equilibrium phenomena can be modeled as Markov processes, minimal free action serves as a basic principle for both equilibrium and non-equilibrium statistical physics.

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arXiv2016

Charge Renormalization and Charge Oscillation in Asymmetric Primitive Model

The Debye charging method is generalized to study the linear response properties of the asymmetric primitive model for electrolytes. Analytic results are obtained for the effective charge distributions of constituent ions inside the electrolyte, from which all static linear response properties of system follow. It is found that, as the ion density increases, both the screening length and the dielectric constant receive substantial renormalization due to ionic correlations. Furthermore, the valence of larger ion is substantially renormalized upwards by ionic correlations, whilst that of smaller ions remains approximately the same. For sufficiently high density, the system exhibit charge oscillations. The threshold ion density for charge oscillation is much lower than the corresponding value for symmetric electrolytes. Our results agree well with large scale Monte Carlo simulations.

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arXiv2016

Particles inside Electrolytes with Ion-specific Interactions, Their Effective Charge Distributions and Effective Interactions

In this work, we explore the statistical physics of colloidal particles that interact with electrolytes via ion-specific interactions. Firstly we study particles interact weakly with electrolyte using linear response theory. We find that the mean potential around a particle is linearly determined by the {\em effective charge distribution} of the particle, which depends both on the bare charge distribution and on ion-specific interactions. We also discuss the effective interaction between two such particles and show that, in far field regime, it is bilinear in the effective charge distributions of two particles. We subsequently generalize the above results to the more complicated case where particles interact strongly with the electrolyte. Our results indicate that in order to understand the statistical physics of non-dilute electrolytes, both ion-specific interactions and ionic correlations have to be addressed in a single unified and consistent framework.

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arXiv2016

Charged Plate in Asymmetric Electrolytes: One-loop Renormalization of Surface Charge Density and Debye Length due to Ionic Correlations

The self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a $m:-n$ electrolyte. A perturbation series is developed in terms of $g = 4 πb/\ell_{\rm {\scriptscriptstyle DB}}$, where $b, \ell_{\rm{\scriptscriptstyle DB}}$ are Bjerrum length and {\em bare} Debye length respectively. To the zeroth order, we obtain nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes ($m \neq n$), the first order (one-loop) correction to mean potential contains a {\em secular term}, which indicates the breakdown of regular perturbation method. Using a renormalizaton group transformation (RG), we remove the secular term and obtain a globally well-behaved one-loop approximation with {\em a renormalized Debye length} and {\em a renormalized surface charge density}. Furthermore, we find that if the counter-ions are multivalent, the surface charge density is renormalized substantially {\em downwards}, and may undergo a change of sign, if the bare surface charge density is sufficiently large.

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