High Rate Regime Research Articles

Asynchronous Communication: Capacity Bounds and Suboptimality of Training

Several aspects of the problem of asynchronous point-to-point communication without feedback are developed when the source is highly intermittent. In the system model of interest, the codeword is transmitted at a random time within a prescribed window whose length corresponds to the level of asynchronism between the transmitter and the receiver. The decoder operates sequentially and communication rate is defined as the ratio between the message size and the elapsed time between when transmission commences and when the decoder makes a decision. For such systems, general upper and lower bounds on capacity as a function of the level of asynchronism are established, and are shown to coincide in some nontrivial cases. From these bounds, several properties of this asynchronous capacity are derived. In addition, the performance of training-based schemes is investigated. It is shown that such schemes, which implement synchronization and information transmission on separate degrees of freedom in the encoding, cannot achieve the asynchronous capacity in general, and that the penalty is particularly significant in the high-rate regime.

The Approximate Capacity of the Gaussian $N$-Relay Diamond Network

We consider the Gaussian “diamond” or parallel relay network, in which a source node transmits a message to a destination node with the help of N relays. Even for the symmetric setting, in which the channel gains to the relays are identical and the channel gains from the relays are identical, the capacity of this channel is unknown in general. The best known capacity approximation is up to an additive gap of order N bits and up to a multiplicative gap of order N2, with both gaps independent of the channel gains. In this paper, we approximate the capacity of the symmetric Gaussian N-relay diamond network up to an additive gap of 1.8 bits and up to a multiplicative gap of a factor 14. Both gaps are independent of the channel gains and, unlike the best previously known result, are also independent of the number of relays N in the network. Achievability is based on bursty amplify-and-forward, showing that this simple scheme is uniformly approximately optimal, both in the low-rate as well as in the high-rate regimes. The upper bound on capacity is based on a careful evaluation of the cut-set bound. We also present approximation results for the asymmetric Gaussian N-relay diamond network. In particular, we show that bursty amplify-and-forward combined with optimal relay selection achieves a rate within a factor O(log4(N)) of capacity with preconstant in the order notation independent of the channel gains.

Enhanced performance of heterogeneous networks through full-duplex relaying

In this article, we focus on the uplink of a heterogeneous network composed of a macrocell and an underlaid femtocell. We address the problem of the interference caused by the macro user (MU) on the femtocell [femto base station (FBS) and users]. The femtocell is composed of an user, a femto relay, which can be seen as another FBS or a dedicated relay, and an FBS. We assume a full-duplex relay (FDR) node which is able to transmit and receive simultaneously while suffering from residual self-interference. We focus on the performance of the femtocell according to different positions of the MU user. We derive closed-form expressions for the outage probability and spectral efficiency (throughput) taking into account the self-interference of the FDR node. Moreover, we assume that the nodes are able to apply successive interference cancellation on the MU signal. Our results show that FDR can considerably enhance the performance of the femtocell, even in the presence of strong self-interference at the FDR, allowing the femtocell to operate in a high rate regime.

Rotated Multi-D Constellations in Rayleigh Fading: Mutual Information Improvement and Pragmatic Approach for Near-Capacity Performance in High-Rate Regions

This paper studies the mutual information improvement attained by rotated multidimensional (multi-D) constellations via a unitary precoder G in Rayleigh fading. At first, based on the symmetric cut-off rate of the N-D signal space, we develop a design criterion with regard to the precoder G. It is then demonstrated that the use of rotated constellations in only a reasonably low dimensional signal space can significantly increase the mutual information in high-rate regimes. Based on parameterizations of unitary matrices, we then construct good unitary precoder G in 4-D signal space using a simple optimization problem, which involves only four real variables and it is applicable to any modulation scheme. To further illustrate the potential of multi-D constellation and to show the practical use of mutual information improvement, we propose a simple yet powerful bit-interleaved coded modulation (BICM) scheme in which a (multi-D) mapping technique employed in a multi-D rotated constellation is concatenated with a short-memory high-rate convolutional code. By using extrinsic information transfer (EXIT) charts, it is shown that the proposed technique provides an exceptionally good error performance. In particular, both EXIT chart analysis and simulation results indicate that a turbo pinch-off and a bit error rate around 10-6 happen at a signal-to-noise ratio that is well below the coded modulation and BICM capacities using traditional signal sets. For example, with code rates ranging from 2/3 to 7/8, the proposed system can operate 0.82 dB-2.93 dB lower than the BICM capacity with QPSK and Gray labeling. The mutual information gain offered by rotated constellations can be therefore utilized to design simple yet near Shannon limit systems in the high-rate regions.

Verification Decoding of High-Rate LDPC Codes With Applications in Compressed Sensing

This paper considers the performance of (j, k)-regular low-density parity-check (LDPC) codes with message-passing (MP) decoding algorithms in the high-rate regime. In particular, we derive the high-rate scaling law for MP decoding of LDPC codes on the binary erasure channel (BEC) and the q-ary symmetric channel (q-SC). For the BEC and a fixed j, the density evolution (DE) threshold of iterative decoding scales like Θ(k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ) and the critical stopping ratio scales like Θ(k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-j/(j-2)</sup> ). For the q-SC and a fixed j, the DE threshold of verification decoding depends on the details of the decoder and scales like Θ(k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ) for one decoder. Using the fact that coding over large finite alphabets is very similar to coding over the real numbers, the analysis of verification decoding is also extended to the compressed sensing (CS) of strictly sparse signals. A DE-based approach is used to analyze the CS systems with randomized-reconstruction guarantees. This leads to the result that strictly sparse signals can be reconstructed efficiently with high probability using a constant oversampling ratio (i.e., when the number of measurements scales linearly with the sparsity of the signal). A stopping-set-based approach is also used to get stronger (e.g., uniform-in-probability) reconstruction guarantees.

LTS and FS Inhibitory Interneurons, Short-Term Synaptic Plasticity, and Cortical Circuit Dynamics

Somatostatin-expressing, low threshold-spiking (LTS) cells and fast-spiking (FS) cells are two common subtypes of inhibitory neocortical interneuron. Excitatory synapses from regular-spiking (RS) pyramidal neurons to LTS cells strongly facilitate when activated repetitively, whereas RS-to-FS synapses depress. This suggests that LTS neurons may be especially relevant at high rate regimes and protect cortical circuits against over-excitation and seizures. However, the inhibitory synapses from LTS cells usually depress, which may reduce their effectiveness at high rates. We ask: by which mechanisms and at what firing rates do LTS neurons control the activity of cortical circuits responding to thalamic input, and how is control by LTS neurons different from that of FS neurons? We study rate models of circuits that include RS cells and LTS and FS inhibitory cells with short-term synaptic plasticity. LTS neurons shift the RS firing-rate vs. current curve to the right at high rates and reduce its slope at low rates; the LTS effect is delayed and prolonged. FS neurons always shift the curve to the right and affect RS firing transiently. In an RS-LTS-FS network, FS neurons reach a quiescent state if they receive weak input, LTS neurons are quiescent if RS neurons receive weak input, and both FS and RS populations are active if they both receive large inputs. In general, FS neurons tend to follow the spiking of RS neurons much more closely than LTS neurons. A novel type of facilitation-induced slow oscillations is observed above the LTS firing threshold with a frequency determined by the time scale of recovery from facilitation. To conclude, contrary to earlier proposals, LTS neurons affect the transient and steady state responses of cortical circuits over a range of firing rates, not only during the high rate regime; LTS neurons protect against over-activation about as well as FS neurons.

Combustion of porous carbon particles in air

Combustion of a carbon particle in air is considered on the basis of a diffusion-kinetic model. Two regimes of combustion are shown to exist: high- and low-rate regimes. In the high-rate combustion regime, oxygen is totally consumed in a homogeneous reaction running above the particle surface and does not reach the particle, whereas carbon is consumed in a reaction with carbon dioxide. In the low-rate combustion regime, oxygen reaches the particle surface, and the reaction of carbon with oxygen producing carbon dioxide runs within the porous particle.

High-Rate Vector Quantization for the Neyman–Pearson Detection of Correlated Processes

This paper investigates the effect of quantization on the performance of the Neyman-Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -point quantizer and transmitted to a decision device which performs a binary hypothesis test. For any false alarm level, it is shown that the miss probability of the Neyman-Pearson test converges to zero exponentially as the number of samples tends to infinity, assuming that the observed process satisfies certain mixing conditions. The main contribution of this paper is to provide a compact closed-form expression of the error exponent in the high-rate regime, i.e., when the number <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> of quantization levels tends to infinity, generalizing previous results of Gupta and Hero to the case of nonindependent observations. If <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> represents the dimension of one sample, it is proved that the error exponent converges at rate <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2/d</sup> to the one obtained in the absence of quantization. As an application, relevant high-rate quantization strategies which lead to a large error exponent are determined. Numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error.

Kinetic Analysis of High-Rate and of Low-Rate Regimes in CO Oxidation on Pt Group Metals: Evidence for Vibrational Excitation of the O-Rich Adlayer and for Thermal Equilibrium of the CO-Rich Phase

Abstract Proper reduction of available literature data on the heterogeneous CO+O2 reaction on Pt group metals allows one to describe the parallel process of CO desorption, in extended intervals of temperature and gas composition, both in the High-Rate regime of an oxygen rich surface and in the Low-Rate regime of a CO rich surface. The outcome of this analysis is the determination of “apparent” as well as of “true” activation energies for both CO oxidation and desorption and their dependence on surface coverage by O or by CO-adspecies. The conclusion is reached that non-equilibrium conditions of vibrational excitation of the adlayers prevail in the HR regions, while Boltzmann equilibrium characterizes LR regimes in extended temperature and pressure intervals. These results have been discussed in the framework of a theoretical model that predicts hyperthermal vibrational states of the adlayer, which depend on the efficiency of energy dissipation into the metal.

Efficient receiver algorithms for DFT-spread OFDM systems

For the 3GPP LTE uplink transmissions, the DFTspread OFDM technique has been adopted as the air interface in order to reduce the peak-to-average-power ratio (PAPR). In this scheme, each data symbol is spread over many tones by a discrete Fourier transform (DFT) operation at the transmitter before being sent to the orthogonal frequency division multiplexing (OFDM) modulator. Moreover, more than one user can be scheduled over the same frequency and time resource block (RB) via space-division multiple-access (SDMA). The conventional receiver technique for such DFT-spread OFDM systems involves tone-by-tone single-tap equalization followed by an inverse DFT operation. In this paper, we propose a more powerful receiver technique for DFT-spread OFDM systems that consists of an efficient linear pre-filter and a two-symbol soft output demodulator. The proposed method can be applied to both single-user per RB (DFT-S-OFDMA) and multiple users per RB (DFT-S-OFDMSDMA) systems and it offers significant performance gains over the conventional method, especially in the high-rate regime, with little attendant increase in computational complexity.

CO Oxidation on Pt-Group Metals from Ultrahigh Vacuum to Near Atmospheric Pressures. 1. Rhodium

The CO oxidation reaction on Rh(111) was studied both at low pressures (≤2 × 10−4 Torr) under steady-state conditions and at high pressures (0.01−88 Torr) in a batch reactor at various gaseous reactant compositions. Surface CO and O coverages were determined using polarization modulation infrared reflection absorption spectroscopy (PM-IRAS) and X-ray photoelectron spectroscopy (XPS). CO titration experiments were also carried out on surfaces with known oxygen coverages. Both CO and O inhibition were evident at low pressures so that only within a relatively narrow temperature range were the reaction conditions optimized such that the CO conversion reached ∼20% of the CO flux to the surface. For high pressures and with stoichiometric or slightly oxidizing reactant ratios (O2/CO ≤ 2), the reaction fell into three regimes: (i) a CO-inhibited low temperature regime where the reaction rate was determined by CO desorption; (ii) a mass transfer limited regime at high temperatures; and (iii) a transient, high-rate regime lying between regimes (i) and (ii) where the reaction was not completely controlled by mass transfer limitation. For all reaction conditions investigated (when O2/CO ≤ 2), the surface oxygen coverage did not exceed ∼0.5 monolayer. With very oxidizing reactants (O2/CO ≥ 5), the reactivity of the Rh surface decreased dramatically at high temperatures due to oxidation. Furthermore, the so-called “superior oxide reactivity” for CO oxidation that has been proposed in several recent studies is not evident in this investigation.

CO oxidation trends on Pt-group metals from ultrahigh vacuum to near atmospheric pressures: A combined in situ PM-IRAS and reaction kinetics study

The CO oxidation reaction on Pt-group metals (Pt, Rh, and Pd) has been investigated at low (⩽10−3Torr) and near atmospheric (1–102Torr) pressures in a batch reactor under steady-state conditions and at various gaseous reactant compositions using PM-IRAS and kinetic measurements. The results indicate that Langmuir–Hinshelwood kinetics adequately provides a general description of the kinetic trends over a wide range of pressures provided that mass transfer effects are considered. At high pressures, the reaction kinetics fall into three regimes: a CO-inhibited low temperature regime where the reaction rate is determined by CO desorption; a mass transfer limited regime at high temperatures; and a transient, high-rate regime which lies in between the other two regimes. The data show that the most reactive surface phase, at both low and high pressures, is a CO-uninhibited phase. This surface phase is not an oxide phase, but a surface phase that contains primarily chemisorbed atomic oxygen and a low coverage of CO.

Routing and Power Allocation in Asynchronous Gaussian Multiple-Relay Channels

We investigate the cooperation efficiency of the multiple-relay channel when carrier-level synchronization is not available and all nodes use a decode-forward scheme. We show that by using decode-forward relay signaling, the transmission is effectively interference-free even when all communications share one common physical medium. Furthermore, for any channel realization, we show that there always exist a sequential path and a corresponding simple power allocation policy, which are optimal. Although this does not naturally lead to a polynomial algorithm for the optimization problem, it greatly reduces the search space and makes finding heuristic algorithms easier. To illustrate the efficiency of cooperation and provide prototypes for practical implementation of relay-channel signaling, we propose two heuristic algorithms. The numerical results show that in the low-rate regime, the gain from cooperation is limited, while the gain is considerable in the high-rate regime.

Rate-adaptive codes for distributed source coding

Source coding with correlated decoder side information is considered. We impose the practical constraint that the encoder be unaware of even the statistical dependencies between source and side information. Two classes of rate-adaptive distributed source codes, both based on low-density parity-check (LDPC) codes, are developed and their design is studied. Specific realizations are shown to be better than alternatives of linear encoding and decoding complexity. The proposed rate-adaptive LDPC accumulate (LDPCA) codes and sum LDPC accumulate (SLDPCA) codes (of length 6336 bits) perform within 10% and 5% of the Slepian–Wolf bound in the moderate and high rate regimes, respectively.

Modes of dynamic shear failure in solids

The technique of loading edge cracks by edge impact (LECEI) for generating high rates of crack tip shear (mode-II) loading is presented. The LECEI-technique in combination with a gas gun for accelerating the impactor is used to study the high rate shear failure behaviour of three types of materials. Epoxy resin (Araldite B) shows failure by tensile cracks up to the highest experimentally achievable loading rate; steel (high strength maraging steel X2 NiCoMo 18 9 5) shows a failure mode transition: at low rates failure occurs by tensile cracks, at higher rates, above a certain limit velocity, failure by adiabatic shear bands is observed; aluminum alloy (Al 7075) shows failure due to shear band processes in the high rate regime, but this failure mode is observed over the entire range of lower loading rates, even down to quasi-static conditions. Characteristics of the failure modes are presented. When transitions are observed in the failure process from tensile cracks to shear bands the limit velocity for failure mode transition depends on the bluntness of the starter crack the failure is initiated from: The larger the bluntness of the starter crack the higher the critical limit velocity for failure mode transition. The data indicate that adiabatic shear bands require and absorb more energy for propagation than tensile cracks. Aspects of the energy balance controlling mode-II instability processes in general are considered. Effects very different than for the mode-I instability process are observed: When failure by a tensile crack occurs under mode-II initiation conditions, a notch is formed between the initiated kinked crack and the original starter crack, and, at this notch a compressive stress concentration builds up. The energy for building up this stress concentration field is not available for propagation of the initiated kinked crack. The energy density of a mode-II crack tip stress field, however, when compared to an equivalent mode-I crack tip field, is considerably larger, and, consequently, the remaining driving energy for any mode-II initiated failure process, nevertheless, is higher than for the case of equivalent mode-I initiation conditions. Furthermore, mode-II crack tip plastic zones are considerably larger than equivalent mode-I crack tip plastic zones. Consequently, validity conditions for linear-elastic or small scale yielding failure behaviour are harder to fulfill and possibilities for the activation of nonlinear high energy ductile type failure processes are enhanced. Speculations on how these effects might favour failure by high energy processes in general and by shear bands processes in particular for conditions of high rate shear mode-II loading are presented.

Transition from the regime of low rates of filtration combustion of gases to the regime of high rates with a pressure increase

Regularities of the transition from the regime of low rates (RLR) of filtration combustion (FC) of gases to the regime of high rates (RHR) with a pressure increase are investigated. It is shown that allowance for gas-phase transfer is important for description of FC, at least when the size of the skeleton pores d>1.5–2.0 mm and the calorific power of the fuel exceeds the limit of propagation of the flame. With an increase of 1–2 atm in the working pressure as compared to atmospheric pressure the critical pore size decreases by a factor of 2.0–2.5. A theoretical model that makes it possible to evaluate the velocities and temperatures of FC stationary waves under conditions of the transition from RLR to RHR and to establish realization limits for these regimes is proposed. It is shown that a more adequate description of the transient regime and the regime of high rates is achieved when the turbulent character of the combustion is allowed for.

Optimal Control Framework for Multistage Endoreversible Engines with Heat and Mass Transfer

We develop a general optimal control framework for a difficult class of problems of work maximization in endoreversible multistage processes which yield mechanical work with finite rates and are characterized by multiple (vectorial) efficiencies. Bellman's method of dynamic programming is used either to construct his recurrence equation or to arrive at a discrete maximum principle of Pontryagin's type, in which a Hamiltonian is maximized with respect to controls. Both these algorithms are powerful computational tools which serve to maximize the power output and evaluate optimal controls. Equations of dynamics which follow from energy and matter balances and transfer equations are difference constraints for optimizing work. Irreversibilities caused by the energy and mass transport are essential. Variation of efficiencies is analyzed in terms of heat and mass fluxes as natural control variables. Enhanced bounds for the work released from an engine system or added to a heat-pump system are evaluated. Lagrangians and Hamiltonians of work functionals and discrete canonical equations are effective; they reach their continuous counterparts in the limit of an infinite number of stages. For a finite-time passage of a resource fluid between two given thermodynamic states, an optimal process is shown to be irreversible. Its optimal intensity is characterized well by the Hamiltonian H. Characteristic functions which describe extremal work are found numerically in terms of final states, process duration and number of stages. An extension of classical exergy to nonisothermal separation systems with a finite number of stages and finite holdup time of the resource fluid is one of the main results. This extended exergy simplifies to the classical thermal exergy in the limit of infinite duration and an infinite number of stages. The extended exergy exhibits a hysteretic property as a decrease of maximum work received from a multistage engine system and an increase of minimum work added to a heat-pump system, two properties which are particularly important in high-rate regimes. This work is a significant step towards a realistic theory of nonisothermal chemical engines.

Generalized Carnot problem of maximum work in finite time via Hamilton–Jacobi–Bellman theory

In this work an irreversible extension of the Carnot problem of maximum mechanical work delivered from a system of two fluids with different temperatures is analysed. We consider the active heat exchange between the fluid of a limited thermal capacity and an ambient or environmental fluid whose thermal capacity is so large that its intensive parameters do not change. In the classical problem the rates vanish due to the reversibility requirement, in the extended problem irreducible irreversibilities occurring in boundary layers are admitted.Our thermodynamic modelling is linked with ideas and methods of the optimal control. A variational theory treats an infinite sequence of infinitesimal Curzon–Ahlborn–Novikov processes (CAN processes) as the pertinent theoretical model leading to a finite time exergy of the system with a finite exchange area or a finite contact time. This dissipative exergy is discussed in terms of the process intensity and finite duration. An analytical formalism, analogous to that in analytical mechanics is effective. A novel approach is worked out based on the Hamilton–Jacobi–Bellman equation for the dissipative exergy and related work functionals (HJB theory). The HJB formulation is helpful to deal with work potentials by numerical methods which use Bellman’s recurrence equation as practically sole method of extremum seeking for functionals with constrained rates and states and for complex boundary conditions.It is pointed out that only an irreversible process can be optimal for a finite duration. A link is shown between the process duration, dissipation and optimal intensity measured in terms of a Hamiltonian. Hysteretic properties are effective which cause the difference between the work supplied and delivered, for inverted end states of the process. A decrease of maximal work received from an engine system and an increase of minimal work added to a heat pump system is shown in the high-rate regimes and for short durations. The results prove that bounds of the classical availability should be replaced by stronger bounds obtained for finite time processes.

Finite time generalization of thermal exergy

An extended exergy allowing some inevitable dissipative properties (e.g. those occurring in boundary layers) can be formulated for finite rate transitions, which lead a system not in equilibrium with the environment (or “dead state”) to equilibrium with it in a finite time. This exergy is a function of the end states and the process duration or a process intensity index. This exergy simplifies to classical thermal exergy in the limiting case of infinite duration, when the property of reversibility is recovered due to the vanishing rates. The functional of the extended exergy can be derived either as a finite time extension of the classical thermodynamic work extracted from a system and its environment or by evaluating a functional of the dissipated classical exergy. With finite time exergy, one can effectively optimize various continuous and multistage processes encountered in the theory of energy conversion and energy exchange in systems with a finite exchange area or with a finite contact time. However, the most important application of the dissipative exergy is the enhanced bounds predicted for the work delivery (consumption) in finite rate processes. These bounds are stronger than classical thermostatic bounds. In our formulation, nonlinear thermodynamic models are linked with ideas and methods of variational calculus. The variational formalism, with certain energy like and momentum like quantities strongly analogous to those known from analytical mechanics and optimal control theory, is an effective tool in the optimization of work. In this theoretical framework, one can easily discuss the role of finite process intensity and finite duration. The optimality of a specific irreversible process for the finite time transition of a fluid from one thermodynamic state to another is pointed out as well as a connection between the process duration, optimal dissipation and the optimal process intensity measured in terms of a Hamiltonian function. Our analysis proves that finite time exergy is different for processes approaching equilibrium with the environment, in which work is released (engine mode) and for processes departing equilibrium in which work is supplied (heat pump mode). However, the coincidence between the dissipative exergies and classical exergy is shown for the quasistatic case. The hysteretic properties of the finite time exergy cause a decrease in the maximum work received from a system in engine mode and an increase of work added to a system in heat pump mode, features which are particularly important in high rate regimes or for short duration thermodynamic processes. These results prove that the limits implied by the classical exergy theory should be replaced by the more realistic, stronger limits which are obtained for finite time processes.

Nonlinear thermokinetics of maximum work in finite time

We show that an extended exergy of the kinetic rather than static origin can be formulated for finite-time transitions, which simplifies to the classical thermal exergy in the limiting case of infinite duration. The extended exergy can be derived either by gauging a functional of the energy dissipation by the classical exergy or as a finite-time extension of the classical thermodynamic work extracted from a system of a body and its environment. With this exergy we consider optimization applications for various active continuous and cascade processes encountered in the theory of the energy exchange through working fluid of an engine, a refrigerator or a heat pump. They refer e.g. to systems with finite exchange area or with a finite contact time, and they clearly show that a complementary economic theory is possible.This theory is a good example of formulation where nonlinear thermodynamic models are linked with ideas and methods of optimal control. Variational approaches strongly analogous to those in analytical mechanics and the optimal control theory of continuous and discrete systems are effective tools in thermodynamics optimization. Nonlinear equations of dynamics, which follow as combinations of the energy balance and transfer equations, are constraints in the problem of work optimization. Functionals, which describe the maximized work, can effectively be optimized by various optimization methods; in this work variational calculus is used along with some aspect of the canonical transformation theory. In particular one can discuss the role of the finite process intensity and finite duration. The optimality of a definite irreversible process for a finite-time transition of a controlled fluid is pointed out as well as a connection between the process duration, optimal dissipation and the optimal process intensity measured in terms of a Hamiltonian. Discrete processes can be analyzed by methods extending those known for continuous ones.The results show that limits of the classical availability theory should be replaced by better limits which are obtained for the finite-time processes and which are closer to reality. A hysteretic property is discovered for the generalized exergy that describes a decrease of the maximum work received from an engine system and an increase of work added to a heat pump system, the features of which are particularly important in high-rate regimes (for short durations of thermodynamic processes).