The fourth law of thermodynamics: steepest entropy ascent

Thermodynamic Stability Theories of Irreversible Processes and the Fourth Law of Thermodynamics

Three approaches for determining the thermodynamic stability of irreversible processes are described in generalized formulations. The simplest is the Gibbs-Duhem theory, specialized to irreversible trajectories, which uses the concept of virtual displacement in the reverse direction. Its only drawback is that even a trajectory leading to an explosion is identified as a thermodynamically stable motion. In the second approach, we use a thermodynamic Lyapunov function and its time rate from the Lyapunov thermodynamic stability theory (LTS, previously known as CTTSIP). In doing so, we demonstrate that the second differential of entropy, a frequently used Lyapunov function, is useful only for investigating the stability of equilibrium states. Nonequilibrium steady states do not qualify. Without using explicit perturbation coordinates, we further identify asymptotic thermodynamic stability and thermodynamic stability under constantly acting disturbances of unperturbed trajectories as well as of nonequilibrium steady states. The third approach is also based on the Lyapunov function from LTS, but here we additionally use the rates of perturbation coordinates, based on the Gibbs relations and without using their explicit expressions, to identify not only asymptotic thermodynamic stability but also thermodynamic stability under constantly acting disturbances. Only those trajectories leading to an infinite rate of entropy production (unstable states) are excluded from this conclusion. Finally, we use these findings to formulate the Fourth Law of thermodynamics based on the thermodynamic stability. It is a comprehensive statement covering all nonequilibrium trajectories, close to as well as far from equilibrium. Unlike previous suggested "fourth laws", this one meets the same level of generality that is associated with the original zeroth to third laws. The above is illustrated using the Schlögl reaction with its multiple steady states in certain regions of operation.

Synthesis, structural, characterization, antibacterial and antibiotic modifying activity, ADMET study, molecular docking and dynamics of chalcone (E)-1-(4-aminophenyl)-3-(4-nitrophenyl)prop-2-en-1-one in strains of Staphylococcus aureus carrying NorA and MepA efflux pumps

Chalcones have an open chain flavonoid structure that can be obtained from natural sources or by synthesis and are widely distributed in fruits, vegetables, and tea. They have a simple and easy to handle structure due to the α-β-unsaturated bridge responsible for most biological activities. The facility to synthesize chalcones combined with its efficient in combating serious bacterial infections make these compounds important agents in the fight against microorganisms. In this work, the chalcone (E)-1-(4-aminophenyl)-3-(4-nitrophenyl)prop-2-en-1-one (HDZPNB) was characterized by spectroscopy and electronic methods. In addition, microbiological tests were performed to investigate the modulator potential and efflux pump inhibition on S. aureus multi-resistant strains. The modulating effect of HDZPNB chalcone in association with the antibiotic norfloxacin, on the resistance of the S. aureus 1199 strain, resulted in increase the MIC. In addition, when HDZPNB was associated with ethidium bromide (EB), it caused an increase in the MIC value, thus not inhibiting the efflux pump. For the strain of S. aureus 1199B, carrying the NorA pump, the HDZPNB associated with norfloxacin showed no modulatory, and when the chalcone was used in association with EB, it had no inhibitory effect on the efflux pump. For the tested strain of S. aureus K2068, which carries the MepA pump, it can be observed that the chalcone together the antibiotic resulted in an increase the MIC. On the other hand, when chalcone was used in association with EB, it caused a decrease in bromide MIC, equal to the reduction caused by standard inhibitors. Thus, these results indicate that the HDZPNB could also act as an inhibitor of the S. aureus gene overexpressing pump MepA. The molecular docking reveals that chalcone has a good binding energies -7.9 for HDZPNB/MepA complexes, molecular dynamics simulations showed that Chalcone/MetA complexes showed good stability of the structure in an aqueous solution, and ADMET study showed that the chalcone has a good oral bioavailability, high passive permeability, low risk of efflux, low clearance rate and low toxic risk by ingestion. The microbiological tests show that the chalcone can be used as a possible inhibitor of the Mep A efflux pump.Communicated by Ramaswamy H. Sarma.

Anxiolytic effects of N-(4,5-dihydro-5-oxo-1,2-dithiolo-[4,3,b]-pyrrole-6-yl)-N-methylformamide, a pyrroloformamide isolated from a marine Streptomyces sp., in adult zebrafish by the 5-HT system

General anxiety disorders are among the most prevalent mental health problems worldwide. The emergence and development of anxiety disorders can be due to genetic (30-50%) or non-genetic (50-70%) factors. Despite medical progress, available pharmacotherapies are sometimes ineffective or can cause undesirable side effects. Thus, it becomes necessary to discover new safe and effective drugs against anxiety. This study evaluated the anxiolytic effect in adult zebrafish (Danio rerio) of a natural pyrroloformamide (PFD), N-(4,5-dihydro-5-oxo-1,2-dithiolo-[4,3,b]-pyrrole-6-yl)-N-methylformamide, isolated from a Streptomyces sp. bacterium strain recovered from the ascidian Eudistoma vannamei. The complete structure of PFD was determined by a detailed NMR analysis, including 1H-13C and 1H-15N-HBMC data. In addition, conformational and DFT computational studies also were performed. A group of fishes (n = 6) was treated orally with PFD (0.1, 0.5 and 1.0 mg/mL; 20 μL) and subjected to locomotor activity and light/dark tests, as well as, acute toxicity 96 h. The involvement of the GABAergic and serotonergic (5-HT) systems was investigated using flumazenil (a silent modulator of GABA receptor) and 5-HT1, 5-HT2A/2C and 5-HTR3A/3B receptors antagonists, known as pizotifen, granisetron and cyproheptadine, respectively. PFD was nontoxic, reduced locomotor activity and promoted the anxiolytic effect in zebrafish. Flumazenil did not inhibit the anxiolytic effect of the PFD via the GABAergic system. This effect was reduced by a pretreatment with pizotifen and granisetron, and was not reversed after treatment with cyproheptadine. Molecular docking and dynamics studies confirmed the interaction of PFD with the 5-HT receptor.Communicated by Ramaswamy H. Sarma.

Predicting Polymer Brush Behavior in Solvents Using the Steepest-Entropy-Ascent Quantum Thermodynamic Framework

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is utilized to study the effects of temperature on polymer brushes. The brushes are represented by a discrete energy spectrum, and energy degeneracies obtained through the replica-exchange Wang-Landau algorithm. The SEAQT equation of motion is applied to the density of states to establish a unique kinetic path from an initial thermodynamic state to a stable equilibrium state. The kinetic path describes the brush's evolution in state space, as it interacts with a thermal reservoir. The predicted occupation probabilities along the kinetic path are used to determine the expected thermodynamic and structural properties. The polymer density profile of a polystyrene brush in cyclohexane solvent is predicted using the equation of motion, and it agrees qualitatively with the experimental density profiles. The Flory-Huggins parameter chosen to describe brush-solvent interactions affects the solvent distribution in the brush but has a minimal impact on the polymer density profile. Three types of nonequilibrium kinetic paths with differing amounts of entropy production are considered: a heating path, a cooling path, and a heating-cooling path. Properties such as tortuosity, radius of gyration, brush density, solvent density, and brush chain conformations are calculated for each path.

Physicochemical Mechanics and Nonequilibrium Chemical Thermodynamics

Equilibrium thermodynamics answers the question, "by how much?" Nonequilibrium thermodynamics answers the question "how fast?" The physicochemical mechanics approach presented in this article answers both of these questions. It also gives equilibrium laws and expressions for all major transport coefficients and their relations, which was previously impossible. For example, Onsager's reciprocal relations only tell us that symmetric transport coefficients are equal, and even for these, the value is often not known. Our new approach, applicable to non-isolated systems, leads to a new formulation of the second law of thermodynamics and agrees with entropy increase in spontaneous processes for isolated systems. Instead of entropy, it is based on a modified Lagrangian formulation which always increases during system evolution, even in the presence of external fields. This article will present numerous examples of physicochemical mechanics can be applied to various transport processes and their equilibriums, including thermodiffusion and different surface processes. It has been proven that the efficiency of a transport process with an actual steady-state flux (as opposed to a reversible process near equilibrium) is 50%. Finally, an analogy between physicochemical mechanics and some social processes is mentioned.

Screening of Potential Inhibitors Targeting the Main Protease Structure of SARS-CoV-2 via Molecular Docking, and Approach with Molecular Dynamics, RMSD, RMSF, H-Bond, SASA and MMGBSA

Severe Acute Respiratory Syndrome caused by a coronavirus is a recent viral infection. There is no scientific evidence or clinical trials to indicate that possible therapies have demonstrated results in suspected or confirmed patients. This work aims to perform a virtual screening of 1430 ligands through molecular docking and to evaluate the possible inhibitory capacity of these drugs about the M^pro protease of Covid-19. The selected drugs were registered with the FDA and available in the virtual drug library, widely used by the population. The simulation was performed using the MolAiCalD algorithm, with a Lamarckian genetic model (GA) combined with energy estimation based on rigid and flexible conformation grids. In addition, molecular dynamics studies were also performed to verify the stability of the receptor-ligand complexes formed through analyses of RMSD, RMSF, H-Bond, SASA, and MMGBSA. Compared to the binding energy of the synthetic redocking coupling (-6.8 kcal/mol/RMSD of 1.34 Å), which was considerably higher, it was then decided to analyze the parameters of only three ligands: ergotamine (-9.9 kcal/mol/RMSD of 2.0 Å), dihydroergotamine (-9.8 kcal/mol/RMSD of 1.46 Å) and olysio (-9.5 kcal/mol/RMSD of 1.5 Å). It can be stated that ergotamine showed the best interactions with the M^pro protease of Covid-19 in the in silico study, showing itself as a promising candidate for treating Covid-19.

Predicting non-equilibrium folding behavior of polymer chains using the steepest-entropy-ascent quantum thermodynamic framework

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is used to explore the influence of heating and cooling on polymer chain folding kinetics. The framework predicts how a chain moves from an initial non-equilibrium state to stable equilibrium along a unique thermodynamic path. The thermodynamic state is expressed by occupation probabilities corresponding to the levels of a discrete energy landscape. The landscape is generated using the Replica Exchange Wang-Landau method applied to a polymer chain represented by a sequence of hydrophobic and polar monomers with a simple hydrophobic-polar amino acid model. The chain conformation evolves as energy shifts among the levels of the energy landscape according to the principle of steepest entropy ascent. This principle is implemented via the SEAQT equation of motion. The SEAQT framework has the benefit of providing insight into structural properties under non-equilibrium conditions. Chain conformations during heating and cooling change continuously without sharp transitions in morphology. The changes are more drastic along non-equilibrium paths than along quasi-equilibrium paths. The SEAQT-predicted kinetics are fitted to rates associated with the experimental intensity profiles of cytochrome c protein folding with Rouse dynamics.

Steepest entropy ascent solution for a continuous-time quantum walker

We consider the steepest entropy ascent (SEA) ansatz to describe the nonlinear thermodynamic evolution of a quantum system. Recently this principle has been dubbed the fourth law of thermodynamics [Beretta, Phil. Trans. R. Soc. A 378, 20190168 (2020)10.1098/rsta.2019.0168]. A unique global equilibrium state exists in this context, and any other state is driven by the maximum entropy generation principle towards this equilibrium. We study the SEA evolution of a continuous-time quantum walker (CTQW) on a cycle graph with N nodes. SEA solutions are difficult to find analytically. We provide an approximate scheme to find a general single-particle evolution equation governed by the SEA principle, whose solution produces dissipation dynamics. We call this scheme the fixed Lagrange's multiplier (FLM) method. In the Bloch sphere representation, we find trajectories traced out by the Bloch vector within the sphere itself. We have discussed these trajectories under various initial conditions for the case of a qubit. A similar dissipative motion is also observed in the case of CTQW, where probability amplitudes have been used to characterize decoherence. Our FLM scheme shows good agreement with numerical results. As we report, in CTQW, a strong delocalization exists for low system relaxation time.

Success versus failure: Efficient heat devices in thermodynamics

Classical equilibrium thermodynamics provides, in a general way, upper Carnot bounds for the performance of energy converters. Nevertheless, to suggest lower bounds is a much more subtle issue, especially when they are related to a definition of convenience. Here, this issue is investigated in a unified way for heat engines, refrigerators, and heat pumps. First, irreversibilities are weighted in the context of heat reservoir stability for irreversible engines by using the thermodynamic distance between minimum energy and maximum entropy steady states. Some stability coefficients can be related to a majorization process and the obtention of Pareto fronts, linking stability and optimization by means of efficiency and entropy due to correlations between system and reservoirs. Second, these findings are interpreted in a very simple context. A region where the heat device is efficient is defined in a general scheme and, below this zone, the heat device is inefficient in the sense that irreversibilities somehow dominate its behavior. These findings allow for a clearer understanding of the role played by some well-known figures of merit in the scope of finite-time and -size optimization. Comparison with experimental results is provided.

Phytoplankton Temporal Strategies Increase Entropy Production in a Marine Food Web Model

We develop a trait-based model founded on the hypothesis that biological systems evolve and organize to maximize entropy production by dissipating chemical and electromagnetic free energy over longer time scales than abiotic processes by implementing temporal strategies. A marine food web consisting of phytoplankton, bacteria, and consumer functional groups is used to explore how temporal strategies, or the lack thereof, change entropy production in a shallow pond that receives a continuous flow of reduced organic carbon plus inorganic nitrogen and illumination from solar radiation with diel and seasonal dynamics. Results show that a temporal strategy that employs an explicit circadian clock produces more entropy than a passive strategy that uses internal carbon storage or a balanced growth strategy that requires phytoplankton to grow with fixed stoichiometry. When the community is forced to operate at high specific growth rates near 2 d⁻¹, the optimization-guided model selects for phytoplankton ecotypes that exhibit complementary for winter versus summer environmental conditions to increase entropy production. We also present a new type of trait-based modeling where trait values are determined by maximizing entropy production rather than by random selection.

Optimizing Our Patients' Entropy Production as Therapy? Hypotheses Originating from the Physics of Physiology

Understanding how nature drives entropy production offers novel insights regarding patient care. Whilst energy is always preserved and energy gradients irreversibly dissipate (thus producing entropy), increasing evidence suggests that they do so in the most optimal means possible. For living complex non-equilibrium systems to create a healthy internal emergent order, they must continuously produce entropy over time. The Maximum Entropy Production Principle (MEPP) highlights nature's drive for non-equilibrium systems to augment their entropy production if possible. This physical drive is hypothesized to be responsible for the spontaneous formation of fractal structures in space (e.g., multi-scale self-similar tree-like vascular structures that optimize delivery to and clearance from an organ system) and time (e.g., complex heart and respiratory rate variability); both are ubiquitous and essential for physiology and health. Second, human entropy production, measured by heat production divided by temperature, is hypothesized to relate to both metabolism and consciousness, dissipating oxidative energy gradients and reducing information into meaning and memory, respectively. Third, both MEPP and natural selection are hypothesized to drive enhanced functioning and adaptability, selecting states with robust basilar entropy production, as well as the capacity to enhance entropy production in response to exercise, heat stress, and illness. Finally, a targeted focus on optimizing our patients' entropy production has the potential to improve health and clinical outcomes. With the implications of developing a novel understanding of health, illness, and treatment strategies, further exploration of this uncharted ground will offer value.

Variational principles and nonequilibrium thermodynamics

Variational principles play a fundamental role in deriving the evolution equations of physics. They work well in the case of non-dissipative evolution, but for dissipative systems, the variational principles are not unique and not constructive. With the methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena and, surprisingly, in several cases, one can also reproduce the Euler-Lagrange form and symplectic structure of the evolution equations for non-dissipative processes. In this work, we examine some demonstrative examples and compare thermodynamic and variational techniques. Then, we argue that, instead of searching for variational principles for dissipative systems, there is another viable programme: the second law alone can be an effective tool to construct evolution equations for both dissipative and non-dissipative processes. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

Nonequilibrium thermodynamics: emergent and fundamental

How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative and ideal theories at all? How far can we reach with the new methods of nonequilibrium thermodynamics? This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.