Thermodynamic definition of mean temperature.

The notion of mean temperature is crucial for a number of fields, including climate science, fluid dynamics, and biophysics. However, so far its correct thermodynamic foundation is lacking or even believed to be impossible. A physically correct definition should not be based on mathematical notions of the means (e.g., the mean geometric or mean arithmetic), because they are not unique, and they ignore the fact that temperature is an ordinal level variable. We offer a thermodynamic definition of the mean temperature that is based upon the following two assumptions. First, the correct definition should necessarily involve equilibration processes in the initially nonequilibrium system. Among such processes, reversible equilibration and fully irreversible equilibration are the two extreme cases. Second, within the thermodynamic approach we assume that the mean temperature is determined mostly by energy and entropy. Together with the dimensional analysis, the two assumptions lead to a definition of the mean temperature that is determined up to a weight factor that can be fixed to 1/2 due to the maximum ignorance principle. The mean temperature for ideal and (van der Waals) nonideal gases with temperature-independent heat capacity is given by a general and compact formula that (besides the initial temperatures) only depends on the heat capacities and concentration of gases. Our method works for any nonequilibrium initial state, not only two-temperature states.

Advantages of one- and two-photon light in inverse scattering.

We study an inverse scattering problem in which the far-field spectral cross correlation functions of scattered fields are used to determine the unknown dielectric susceptibility of the scattering object. One-photon states for the incident field can resolve (at 100% visibility) twice as many Fourier components of the susceptibility compared with the (naïve) Rayleigh estimate, provided that the measurement is performed in the back-scattering regime. Coherent states are not capable of reaching this optimal resolution (or do so with negligible visibility). Using two-photon states improves upon the one-photon resolution, but the improvement (at 100% visibility) is smaller than twice, and it demands prior information on the object. This improvement can also be realized via two independent laser fields. The dependence on the prior information can be decreased (but not eliminated completely) upon using entangled states of two photons.

Thermodynamic selection: mechanisms and scenarios.

Thermodynamic selection is an indirect competition between agents feeding on the same energy resource and obeying the laws of thermodynamics. We examine scenarios of this selection, where the agent is modeled as a heat-engine coupled to two thermal baths and extracting work from the high-temperature bath. The agents can apply different work-extracting, game-theoretical strategies, e.g. the maximum power or the maximum efficiency. They can also have a fixed structure or be adaptive. Depending on whether the resource (i.e. the high-temperature bath) is infinite or finite, the fitness of the agent relates to the work-power or the total extracted work. These two selection scenarios lead to increasing or decreasing efficiencies of the work-extraction, respectively. The scenarios are illustrated via plant competition for sunlight, and the competition between different ATP production pathways. We also show that certain general concepts of game-theory and ecology-the prisoner's dilemma and the maximal power principle-emerge from the thermodynamics of competing agents. We emphasize the role of adaptation in developing efficient work-extraction mechanisms.

Work Extraction from Fluid Flow: The Analog of Carnot's Efficiency.

Aiming to explore physical limits of wind turbines, we develop a model for determining the work extractable from a compressible fluid flow. The model employs conservation of mass, energy, and entropy and leads to a universal bound for the efficiency of the work extractable from kinetic energy. The bound is reached for a sufficiently slow, weakly forced quasi-one-dimensional, dissipationless flow. In several respects the bound is similar to the Carnot limit for the efficiency of heat engines. More generally, we show that the maximum work-extraction demands a contribution from the enthalpy, and is reached for sonic output velocities and strong forcing.

Defining the Work Done on an Electromagnetic Field.

The problem of defining work done on an electromagnetic field (EMF) via moving charges does not have a ready solution, because the standard Hamiltonian of an EMF-whose time derivative should define the work according to the first law-is not gauge invariant. This limits applications of statistical mechanics to an EMF. We obtained a new, explicitly gauge-invariant Hamiltonian for an EMF that depends only on physical observables. This Hamiltonian allows us to define work and to formulate the second law for an EMF. It also leads to a direct link between this law and the electrodynamic arrow of time, i.e., choosing retarded, and not advanced solutions of wave equations. Measuring the thermodynamic work can determine whether the photon mass is small but nonzero.

Adaptive Heat Engine.

A major limitation of many heat engines is that their functioning demands on-line control and/or an external fitting between the environmental parameters (e.g., temperatures of thermal baths) and internal parameters of the engine. We study a model for an adaptive heat engine, where-due to feedback from the functional part-the engine's structure adapts to given thermal baths. Hence, no on-line control and no external fitting are needed. The engine can employ unknown resources; it can also adapt to results of its own functioning that make the bath temperatures closer. We determine resources of adaptation and relate them to the prior information available about the environment.

Time arrow is influenced by the dark energy.

The arrow of time and the accelerated expansion are two fundamental empirical facts of the universe. We advance the viewpoint that the dark energy (positive cosmological constant) accelerating the expansion of the universe also supports the time asymmetry. It is related to the decay of metastable states under generic perturbations, as we show on example of a microcanonical ensemble. These states will not be metastable without dark energy. The latter also ensures a hyperbolic motion leading to dynamic entropy production with the rate determined by the cosmological constant.

Thermal-induced force release in oxyhemoglobin.

Oxygen is released to living tissues via conformational changes of hemoglobin from R-state (oxyhemoglobin) to T-state (desoxyhemoglobin). The detailed mechanism of this process is not yet fully understood. We have carried out micromechanical experiments on oxyhemoglobin crystals to determine the behavior of the Young's modulus and the internal friction for temperatures between 20 °C and 70 °C. We have found that around 49 °C oxyhemoglobin crystal samples undergo a sudden and strong increase of their Young's modulus, accompanied by a sudden decrease of the internal friction. This sudden mechanical change (and the ensuing force release) takes place in a partially unfolded state and precedes the full denaturation transition at higher temperatures. After this transformation, the hemoglobin crystals have the same mechanical properties as their initial state at room temperatures. We conjecture that it can be relevant for explaining the oxygen-releasing function of native oxyhemoglobin when the temperature is increased, e.g. due to active sport. The effect is specific for the quaternary structure of hemoglobin, and is absent for myoglobin with only one peptide sequence.

Memory-induced mechanism for self-sustaining activity in networks.

We study a mechanism of activity sustaining on networks inspired by a well-known model of neuronal dynamics. Our primary focus is the emergence of self-sustaining collective activity patterns, where no single node can stay active by itself, but the activity provided initially is sustained within the collective of interacting agents. In contrast to existing models of self-sustaining activity that are caused by (long) loops present in the network, here we focus on treelike structures and examine activation mechanisms that are due to temporal memory of the nodes. This approach is motivated by applications in social media, where long network loops are rare or absent. Our results suggest that under a weak behavioral noise, the nodes robustly split into several clusters, with partial synchronization of nodes within each cluster. We also study the randomly weighted version of the models where the nodes are allowed to change their connection strength (this can model attention redistribution) and show that it does facilitate the self-sustained activity.

Nonequilibrium quantum fluctuations of work.

The concept of work is basic for statistical thermodynamics. To gain a fuller understanding of work and its (quantum) features, it needs to be represented as an average of a fluctuating quantity. Here I focus on the work done between two moments of time for a thermally isolated quantum system driven by a time-dependent Hamiltonian. I formulate two natural conditions needed for the fluctuating work to be physically meaningful for a system that starts its evolution from a nonequilibrium state. The existing definitions do not satisfy these conditions due to issues that are traced back to noncommutativity. I propose a definition of fluctuating work that is free of previous drawbacks and that applies for a wide class of nonequilibrium initial states. It allows the deduction of a generalized work-fluctuation theorem that applies for an arbitrary (out-of-equilibrium) initial state.

How adsorption influences DNA denaturation.

The thermally induced denaturation of DNA in the presence of an attractive solid surface is studied. The two strands of DNA are modeled via two coupled flexible chains without volume interactions. If the two strands are adsorbed on the surface, the denaturation phase transition disappears. Instead, there is a smooth crossover to a weakly naturated state. Our second conclusion is that even when the interstrand attraction alone is too weak for creating a naturated state at the given temperature and also when the surface-strand attraction alone is too weak for creating an adsorbed state, the combined effect of the two attractions can lead to a naturated and adsorbed state.

Thermal (in)stability of type I collagen fibrils.

We measured the Young's modulus at temperatures ranging from 20 to 100 degrees C for a collagen fibril that is taken from a rat's tendon. The hydration change under heating and the damping decrement were measured as well. At physiological temperatures 25 to 45 degrees C, the Young's modulus decreases, which can be interpreted as an instability of the collagen. For temperatures between 45 and 80 degrees C, the Young's modulus first stabilizes and then increases when the temperature is increased. The hydrated water content and the damping decrement have strong maximums in the interval 70 to 80 degrees C indicating complex intermolecular structural changes in the fibril. All these effects disappear after heat-denaturation of the sample at 120 degrees C. Our main achievement is a five-stage mechanism by which the instability of a single collagen at physiological temperatures is compensated by the interaction between collagen molecules.

Minimal-work principle and its limits for classical systems.

The minimal-work principle asserts that work done on a thermally isolated equilibrium system is minimal for the slowest (adiabatic) realization of a given process. This principle, one of the formulations of the second law, is operationally well defined for any finite (few particle) Hamiltonian system. Within classical Hamiltonian mechanics, we show that the principle is valid for a system of which the observable of work is an ergodic function. For nonergodic systems the principle may or may not hold, depending on additional conditions. Examples displaying the limits of the principle are presented and their direct experimental realizations are discussed.

Explanation of the Gibbs paradox within the framework of quantum thermodynamics.

The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small difference, but vanishes for identical gases. The resolution offered in the literature, with help of quantum mixing entropy, was later shown to be unsatisfactory precisely where it sought to resolve the paradox. Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining the paradox, since it does not deal explicitly with the difference between the gases. The proper approach employs quantum thermodynamics, which deals with finite quantum systems coupled to a large bath and a macroscopic work source. Within quantum thermodynamics, entropy generally loses its dominant place and the target of the paradox is naturally shifted to a decrease of the maximally available work before and after mixing (mixing ergotropy). In contrast to entropy this is an unambiguous quantity. For almost identical gases the mixing ergotropy continuously goes to zero, thus resolving the paradox. In this approach the concept of "difference between the gases" gets a clear operational meaning related to the possibilities of controlling the involved quantum states. Difficulties which prevent resolutions of the paradox in its entropic formulation do not arise here. The mixing ergotropy has several counterintuitive features. It can increase when less precise operations are allowed. In the quantum situation (in contrast to the classical one) the mixing ergotropy can also increase when decreasing the degree of mixing between the gases or when decreasing their distinguishability. These points go against a direct association of physical irreversibility with lack of information.

Anomalous latent heat in nonequilibrium phase transitions.

We study first-order phase transitions in a two-temperature system, where due to the time-scale separation all the basic thermodynamical quantities (free energy, entropy, etc.) are well defined. The sign of the latent heat is found to be counterintuitive: it is positive when going from the phase where the temperatures and the entropy are higher to the one where these quantities are lower. The effect exists only out of equilibrium and requires conflicting interactions. It is displayed on a lattice gas model of ferromagnetically interacting spin-1/2 particles.

Adhesion-induced DNA naturation.

DNA adsorption and naturation is modeled via two interacting flexible homopolymers coupled to a solid surface. DNA denatures if the entropy gain for unbinding the two strands overcomes the loss of binding energy. When adsorbed to a surface, the entropy gain is smaller than in the bulk, leading to a stronger binding and, upon neglecting self-avoidance, absence of a denatured phase. Now consider conditions where the binding potentials are too weak for naturation, and the surface potential too weak to adsorb single strands. In a variational approach it is shown that their combined action may lead to a naturated adsorbed phase. Conditions for the absence of naturation and adsorption are derived too. The phase diagram is constructed qualitatively.

Fluctuations of work from quantum subensembles: the case against quantum work-fluctuation theorems.

We study how Thomson's formulation of the second law of thermodynamics (no work is extracted from an equilibrium ensemble by a cyclic process) emerges in the quantum situation through the averaging over fluctuations of work. The latter concept is carefully defined for an ensemble of quantum systems, the members of which interact with macroscopic sources of work. The approach is based on splitting a mixed quantum ensemble into pure subensembles, which according to quantum mechanics are maximally complete and irreducible. The splitting is done by filtering the outcomes of a measurement process. The approach is corroborated by comparing to relevant experiments in quantum optics. A critical review is given of two other approaches to fluctuations of work proposed in the literature. It is shown that in contrast to those, the present definition (i) is consistent with the physical meaning of the concept of work as mechanical energy lost by the macroscopic sources, or, equivalently, as the average energy acquired by the ensemble; (ii) applies to an arbitrary nonequilibrium state. There is no direct generalization of the classical work-fluctuation theorem to the proper quantum domain. This implies nonclassical scenarios for the emergence of the second law.

Work extraction in the spin-boson model.

We show that work can be extracted from a two-level system (spin) coupled to a bosonic thermal bath. This is possible due to different initial temperatures of the spin and the bath, both positive (no spin population inversion), and is realized by means of a suitable sequence of sharp pulses applied to the spin. The extracted work can be of the order of the response energy of the bath, therefore much larger than the energy of the spin. Moreover, the efficiency of extraction can be very close to its maximum, given by the Carnot bound, at the same time the overall amount of the extracted work is maximal. Therefore, we get a finite power at efficiency close to the Carnot bound. The effect comes from the back-reaction of the spin on the bath, and it survives for a strongly disordered (inhomogeneously broadened) ensemble of spins. It is connected with generation of coherences during the work-extraction process, and we deduced it in an exactly solvable model. All the necessary general thermodynamical relations are deduced from the first principles of quantum mechanics and connections are made with processes of lasing without inversion and with quantum heat engines.

Minimal work principle: proof and counter-examples.

The minimal work principle states that work done on a thermally isolated equilibrium system is minimal for adiabatically slow (reversible) realization of a given process. This principle, one of the formulations of the second law, is studied here for finite (possibly large) quantum systems interacting with macroscopic sources of work. It is shown to be valid as long as the adiabatic energy levels do not cross. If level crossing does occur, counter-examples are discussed, showing that the minimal work principle can be violated and that optimal processes are neither adiabatically slow nor reversible. The results are corroborated by an exactly solvable model.

Unzipping of DNA with correlated base sequence.

We consider force-induced unzipping transition for a heterogeneous DNA model with a correlated base sequence. Both finite-range and long-range correlated situations are considered. It is shown that finite-range correlations increase stability of DNA with respect to the external unzipping force. Due to long-range correlations the number of unzipped base pairs displays two widely different scenarios depending on the details of the base sequence: either there is no unzipping phase transition at all, or the transition is realized via a sequence of jumps with magnitude comparable to the size of the system. Both scenarios are different from the behavior of the average number of unzipped base pairs (non-self-averaging). The results can be relevant for explaining the biological purpose of correlated structures in DNA.