Refined Second Law of Thermodynamics for Fast Random Processes

We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport and becomes relevant for processes far from quasi-stationary regime. General discussion is illustrated by numerical analysis of the optimal memory erasure protocol for a model for micron-size particle manipulated by optical tweezers.     

A Rather General Variational Principle for Purely Dissipative Non-Stationary Processes

A general variational principle concerning non-stationary purely dissipative phenomena, obeying ONSAGER 's reciprocal relations, is presented. The principle expresses that the variation of the sum of the total entropy production and the time derivative of the MASSIEU function is equal to zero. It is shown that the EULER -LAGRANGE equations corresponding to arbitrary variations of the state variables yield the conservation laws. Other general criteria for non-stationary processes have been given by GLANSDORFF -PRIGOGINE and GYARMATI . They are compared with our principle. Two illustrative examples are considered: coupled heat and electrical conduction in an isotropic medium and chemical reactions coupled with diffusion of matter and heat conduction in a multi-component fluid.     

The Second Law of Thermodynamics: Foundations and Status

Over the last 10–15 years the second law of thermodynamics has undergone unprecedented scrutiny, particularly with respect to its universal status. This brief article introduces the proceedings of a recent symposium devoted to this topic, The second law of thermodynamics: Foundations and Status, held at University of San Diego as part of the 87th Annual Meeting of the Pacific Division of the AAAS (June 19–22, 2006). The papers are introduced under three themes: ideal gases, quantum perspectives, and interpretation. Roughly half the papers support traditional interpretations of the second law while the rest challenge it. Symposium proceedings from 87th Annual Meeting of the Pacific Division of the AAAS; University of San Diego, June 19–22, 2006; D.P. Sheehan, editor.     

Caratheodory and the Foundations of Thermodynamics and Statistical Physics

Constantin Caratheodory offered the first systematic and contradiction free formulation of thermodynamics on the basis of his mathematical work on Pfaff forms. Moreover, his work on measure theory provided the basis for later improved formulations of thermodynamics and physics of continua where extensive variables are measures and intensive variables are densities. Caratheodory was the first to see that measure theory and not topology is the natural tool to understand the difficulties (ergodicity, approach to equilibrium, irreversibility) in the Foundations of Statistical Physics. He gave a measure-theoretic proof of Poincaré's recurrence theorem in 1919. This work paved the way for Birkhoff to identify later ergodicity as metric transitivity and for Koopman and von Neumann to introduce spectral analysis of dynamical systems in Hilbert spaces. Mixing provided an explanation of the approach to equilibrium but not of irreversibility. The recent extension of spectral theory of dynamical systems to locally convex spaces, achieved by the Brussels–Austin groups, gives new nontrivial time asymmetric spectral decompositions for unstable and/or non-integrable systems. In this way irreversibility is resolved in a natural way.     

Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes

We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x,σ)∈Ω×Γ, Ω being a region in ℝ ^d or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601, 2001; J. Stat. Phys. 107(3–4):635–675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at , 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti–Cohen-type symmetry relation with involution map different from time-reversal.     

Functional Interdependence in Coupled Dissipative Structures: Physical Foundations of Biological Coordination

Coordination within and between organisms is one of the most complex abilities of living systems, requiring the concerted regulation of many physiological constituents, and this complexity can be particularly difficult to explain by appealing to physics. A valuable framework for understanding biological coordination is the coordinative structure, a self-organized assembly of physiological elements that collectively performs a specific function. Coordinative structures are characterized by three properties: (1) multiple coupled components, (2) soft-assembly, and (3) functional organization. Coordinative structures have been hypothesized to be specific instantiations of dissipative structures, non-equilibrium, self-organized, physical systems exhibiting complex pattern formation in structure and behaviors. We pursued this hypothesis by testing for these three properties of coordinative structures in an electrically-driven dissipative structure. Our system demonstrates dynamic reorganization in response to functional perturbation, a behavior of coordinative structures called reciprocal compensation. Reciprocal compensation is corroborated by a dynamical systems model of the underlying physics. This coordinated activity of the system appears to derive from the system’s intrinsic end-directed behavior to maximize the rate of entropy production. The paper includes three primary components: (1) empirical data on emergent coordinated phenomena in a physical system, (2) computational simulations of this physical system, and (3) theoretical evaluation of the empirical and simulated results in the context of physics and the life sciences. This study reveals similarities between an electrically-driven dissipative structure that exhibits end-directed behavior and the goal-oriented behaviors of more complex living systems.     

Generalized Second Law of Thermodynamics in Emergent Universe

In this letter, we have considered the FRW model of the emergent universe, which was presented in our previous work (Debnath, in Class. Quantum Gravity 25:205019, 2008). We have chosen one of the form of scale factor in such a way that the emergent scenario is possible in the universe. We have also considered the universe as a thermodynamical system with the horizon surface as a boundary of the system. The entropy and the radius of the event horizon have been calculated in the emergent scenario. When the emergent scenario occurs, we have shown that the generalized second law of thermodynamics is always satisfied for open, flat and closed models of the universe.     

Book Review: Modern Thermodynamics: From Heat Engines to Dissipative Structures

Journal of Statistical Physics -     

Modified Black Hole Thermodynamics with Generalized Uncertainty Principle

In this paper we propose a way of determining the subleading corrections to the Bekenstein-Hawking black hole entropy by considering a modified generalized uncertainty principle with two parameters. In the context of modified generalized uncertainty principle, coefficients of the correction terms of black hole entropy are written in terms of combination of the parameters. We also obtained the corrections to the Stefan-Boltzman law and the black hole evaporation in terms of the parameters. By estimating those parameters, say by experiment, one can test results from other context of quantum gravity theories such as black hole entropy.     

Analogues of Coherent and Dissipative Structures in Social and Historical Processes

An analogy between social and hydrodynamic processes is developed. The relation of the state system to the passionarity theory suggested by L. N. Gumilev is discussed.     

Generalized Integral Fluctuation Relation with Feedback Control for Diffusion Processes

We extend a generalized integral fluctuation relation in diffusion processes that we obtained previously to the situation with feedback control. The general relation not only covers existing results but also predicts other unnoticed fluctuation relations. In addition, we find that its explanation of time-reversal automatically emerges in the derivation. This interesting observation leads into an alternative inequality about the entropy-like quantity with an improved lower bound. Two feedback-controlled Brownian models are used to verify the result.     

Generalized Second Law of Thermodynamics on the Event Horizon for Interacting Dark Energy

Here we are trying to find the conditions for the validity of the generalized second law of thermodynamics (GSLT) assuming the first law of thermodynamics on the event horizon in both cases when the FRW universe is filled with interacting two fluid system- one in the form of cold dark matter and the other is either holographic dark energy or new age graphic dark energy.     

Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces

The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in corresponding limits, the relativistic nonequilibrium thermodynamics with local anisotropy. This leads to a unified formulation of the kinetic equations on (pseudo) Riemannian spaces and in various higher dimensional models of Kaluza–Klein type and/or generalized Lagrange and Finsler spaces. The transition rate considered for the locally anisotropic transport equations is related to the differential cross section and spacetime parameters of anisotropy. The equations of states for pressure and energy in locally anisotropic thermodynamics are derived. The obtained general expressions for heat conductivity, shear, and volume viscosity coefficients are applied to determine the transport coefficients of cosmic fluids in spacetimes with generic local anisotropy. We emphasize that such local anisotropic structures are induced also in general relativity if we are modelling physical processes with respect to frames with mixed sets of holonomic and anholonomic basis vectors which naturally admits an associated nonlinear connection structure.     

Thermodynamics of Black Holes and the Symmetric Generalized Uncertainty Principle

In this paper, we have investigated the thermodynamics of Schwarzschild and Reissner-Nordström black holes using the symmetric generalised uncertainty principle which contains correction terms involving momentum and position uncertainty. The mass-temperature relationship and the heat capacity for these black holes have been computed using which the critical and remnant masses have been obtained. The entropy is found to satisfy the area law upto leading order logarithmic corrections and corrections of the form A² (which is a new finding in this paper) from the symmetric generalised uncertainty principle.     

On the Generalized Heat Conduction Laws in the Reversible Thermodynamics of a Continuous Medium

Doklady Physics - A general covariance variational model of reversible thermodynamics is developed in which the kinematic and force variables are the components of unified tensor objects in the...     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi(LTB) cosmology supported by a perfect Suid source.This model is the natural generalization of the Sat Friedmann-Robertson-Walker(FRW) universe,and describes an inhomogeneous universe with spherical symmetry.After reviewing some basic equations in the parabolic LTB cosmology,we obtain a relation for the deceleration parameter in this model.We also obtain a condition for which the universe undergoes an accelerating phase at the present time.We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology.We find out that in LTB model of cosmology,the apparent horizon's entropy could be feeded by a term,which incorporates the effects of the inhomogeneity.We consider this result and get a relation for the total entropy evolution,which is used to examine the generalized second law of thermodynamics for an accelerating universe.We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi (LTB) cosmology supported by a perfect fluid source. This model is the natural generalization of the flat Friedmann-Robertson-Walker (FRW) universe, and describes an inhomogeneous universe with spherical symmetry. After reviewing some basic equations in the parabolic LTB cosmology, we obtain a relation for the deceleration parameter in this model. We also obtain a condition for which the universe undergoes an accelerating phase at the present time. We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology. We find out that in LTB model of cosmology, the apparent horizon's entropy could be feeded by a term, which incorporates the effects of the inhomogeneity. We consider this result and get a relation for the total entropy evolution, which is used to examine the generalized second law of thermodynamics for an accelerating universe. We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.