The Thermodynamic Covariance Principle

The concept of {\it equivalent systems} from the thermodynamic point of view, originally introduced by Th. De Donder and I. Prigogine, is deeply investigated and revised. From our point of view, two systems are thermodynamically equivalent if, under transformation of the thermodynamic forces, both the entropy production and the Glansdorff-Prigogine dissipative quantity remain unaltered. This kind of transformations may be referred to as the {\it Thermodynamic Coordinate Transformations} (TCT). The general class of transformations satisfying the TCT is determined. We shall see that, also in the nonlinear region ({\it i.e.}, out of the Onsager region), the TCT preserve the reciprocity relations of the transformed transport matrix. The equivalent character of two transformations under TCT, leads to the concept of {\it Thermodynamic Covariance Principle} (TCP) stating that all thermodynamic equations involving the thermodynamic forces and flows ({\it e.g.}, the closure flux-force relations) should be covariant under TCT.Comment: 11 pages, 0 figures. arXiv admin note: text overlap with arXiv:0901.4042, arXiv:0805.326

Information processing in biological molecular machines

Biological molecular machines are bi-functional enzymes that simultaneously catalyze two processes: one providing free energy and second accepting it. Recent studies show that most protein enzymes have a rich dynamics of stochastic transitions between the multitude of conformational substates that make up their native state. It often manifests in fluctuating rates of the catalyzed processes and the presence of short-term memory resulting from the preference of selected conformations. For any stochastic protein machine dynamics we proved a generalized fluctuation theorem that leads to the extension of the second law of thermodynamics. Using them to interpret the results of random walk on a complex model network, we showed the possibility of reducing free energy dissipation at the expense of creating some information stored in memory. The subject of our analysis is the time course of the catalyzed processes expressed by sequences of jumps at random moments of time. Since similar signals can be registered in the observation of real systems, all theses of the paper are open to experimental verification. From a broader physical point of view, the division of free energy into the operation and organization energies is worth emphasizing. Information can be assigned a physical meaning of a change in the value of both these functions of state.Comment: The manuscript contains 14 pages, 7 figure

Derivation of Reference Distribution Functions for Tokamak-plasmas by Statistical Thermodynamics

A general approach for deriving the expression of reference distribution functions by statistical thermodynamics is illustrated, and applied to the case of a magnetically confined plasma. The local equilibrium is defined by imposing the minimum entropy production, which applies only to the linear regime near a stationary thermodynamically non-equilibrium state and the maximum entropy principle under the scale invariance restrictions. This procedure may be adopted for a system subject to an arbitrary number of thermodynamic forces, however, for concreteness, we analyze, afterwords, a magnetically confined plasma subject to three thermodynamic forces, and three energy sources: i) the total Ohmic heat, supplied by the transformer coil, ii) the energy supplied by Neutral Beam Injection (NBI), and iii) the RF energy supplied by Ion Cyclotron Resonant Heating (ICRH) system which heats the minority population. In this limit case, we show that the derived expression of the distribution function is more general than that one, which is currently used for fitting the numerical steady-state solutions obtained by simulating the plasma by gyro-kinetic codes. An application to a simple model of fully ionized plasmas submitted to an external source is discussed. Through kinetic theory, we fixed the values of the free parameters linking them with the external power supplies. The singularity at low energy in the proposed distribution function is related to the intermittency in the turbulent plasma.Comment: 33 pages and 13 figure

Biological molecular machines can process information to reduce energy losses

Biological molecular machines are enzymes that simultaneously catalyze two processes, one donating free energy and second accepting it. Recent studies show that most native protein enzymes have a rich stochastic dynamics that often manifests in fluctuating rates of the catalyzed processes and the presence of short-term memory resulting from transient non-ergodicity. For such dynamics, we prove the generalized fluctuation theorem predicting a possible reduction of energy dissipation at the expense of creating some information stored in memory. The theoretical relationships are verified in computer simulations of random walk on a model critical complex network. The transient utilization of memory may turn out to be crucial for the movement of protein motors and the reason for most protein machines to operate as dimers or higher organized assemblies. From a broader physical point of view, the division of free energy into the operation and organization energy is worth emphasizing. Information can be assigned a physical meaning of a change in the value of both these functions of state.Comment: 19 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1707.0749

On the multi-physics of mass-transfer across fluid interfaces

Mass transfer of gaseous components from rising bubbles to the ambient liquid can be described based on continuum mechanical sharp-interface balances of mass, momentum and species mass. In this context, the standard model consists of the two-phase Navier-Stokes equations for incompressible fluids with constant surface tension, complemented by reaction-advection-diffusion equations for all constituents, employing Fick's law. This standard model is inconsistent with the continuity equation, the momentum balance and the second law of thermodynamics. The present paper reports on the details of these severe shortcomings and provides thermodynamically consistent model extensions which are required to capture various phenomena which occur due to the multi-physics of interfacial mass transfer. In particular, we provide a simple derivation of the interface Maxwell-Stefan equations which does not require a time scale separation, while the main contribution is to show how interface concentrations and interface chemical potentials mediate the influence on mass transfer of a transfer component exerted by the change in interface energy due to an adsorbing surfactant

Broken detailed balance and non-equilibrium dynamics in living systems

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.Comment: 34 pages, 16 figures, review articl

Cycle representatives for the coarse-graining of systems driven into a non-equilibrium steady state

A major current challenge poses the systematic construction of coarse-grained models that are dynamically consistent, and, moreover, might be used for systems driven out of thermal equilibrium. Here we present a novel prescription that extends the Markov state modelling approach to driven systems. The first step is to construct a complex network of microstates from detailed atomistic simulations with transition rates that break detailed balance. The coarse-graining is then carried out in the cycle space of this network. To this end we introduce the concept of representatives, which stand for many cycles with similar properties. We show how to find these cycle communities using well-developed standard algorithms. Removing all cycles except for the representatives defines the coarse-grained model, which is mapped back onto a network with far fewer states and renormalized transition rates that, however, preserve the entropy production of the original network. Our approach is illustrated and validated for a single driven particle

On the Interface Formation Model for Dynamic Triple Lines

This paper revisits the theory of Y. Shikhmurzaev on forming interfaces as a continuum thermodynamical model for dynamic triple lines. We start with the derivation of the balances for mass, momentum, energy and entropy in a three-phase fluid system with full interfacial physics, including a brief review of the relevant transport theorems on interfaces and triple lines. Employing the entropy principle in the form given in [Bothe & Dreyer, Acta Mechanica, doi:10.1007/s00707-014-1275-1] but extended to this more general case, we arrive at the entropy production and perform a linear closure, except for a nonlinear closure for the sorption processes. Specialized to the isothermal case, we obtain a thermodynamically consistent mathematical model for dynamic triple lines and show that the total available energy is a strict Lyapunov function for this system

Hidden entropy production by fast variables

We investigate nonequilibrium underdamped Langevin dynamics of Brownian particles that interact through a harmonic potential with coupling constant $K$ and are in thermal contact with two heat baths at different temperatures. The system is characterized by a net heat flow and an entropy production in the steady state. We compare the entropy production of the harmonic system with that of Brownian particles linked with a rigid rod. The harmonic system may be expected to reduce to the rigid rod system in the infinite $K$ limit. However, we find that the harmonic system in the $K\to\infty$ limit produces more entropy than the rigid rod system. The harmonic system has the center of mass coordinate as a slow variable and the relative coordinate as a fast variable. By identifying the contributions of the degrees of freedom to the total entropy production, we show that the hidden entropy production by the fast variable is responsible for the extra entropy production. We discuss the $K$ dependence of each contribution.Comment: 6 pages, 3 figure

The Measure-theoretic Identity Underlying Transient Fluctuation Theorems

We prove a measure-theoretic identity that underlies all transient fluctuation theorems (TFTs) for entropy production and dissipated work in inhomogeneous deterministic and stochastic processes, including those of Evans and Searles, Crooks, and Seifert. The identity is used to deduce a tautological physical interpretation of TFTs in terms of the arrow of time, and its generality reveals that the self-inverse nature of the various trajectory and process transformations historically relied upon to prove TFTs, while necessary for these theorems from a physical standpoint, is not necessary from a mathematical one. The moment generating functions of thermodynamic variables appearing in the identity are shown to converge in general only in a vertical strip in the complex plane, with the consequence that a TFT that holds over arbitrary timescales may fail to give rise to an asymptotic fluctuation theorem for any possible speed of the corresponding large deviation principle. The case of strongly biased birth-death chains is presented to illustrate this phenomenon. We also discuss insights obtained from our measure-theoretic formalism into the results of Saha et. al. on the breakdown of TFTs for driven Brownian particles