Violation of the Zeroth Law of Thermodynamics in Systems with Negative Specific Heat (original) (raw)
Related papers
Negative specific heat in out-of-equilibrium nonextensive systems
2002
We discuss the occurrence of negative specific heat in a nonextensive system which has an equilibrium second-order phase transition. The specific heat is negative only in a transient regime before equilibration , in correspondence to long-lasting metastable states. For these states standard equilibrium Bolzmann-Gibbs thermodynamics does not apply and the system shows non-Gaussian velocity distributions, anomalous diffusion and correlation in phase space. Similar results have recently been found also in several other nonextensive systems, supporting the general validity of this scenario. These models seem also to support the conjecture that a nonexstensive statistical formalism, like the one proposed by Tsallis, should be applied in such cases. The theoretical scenario is not completely clear yet , but there are already many strong theoretical indications suggesting that, it can be wrong to consider the observation of an experimental negative specific heat as an unique and unambiguous signature of a standard equilibrium first-order phase transition.
Feeding upon negative entropy in a thermal-equilibrium environment
The validity of the Second Law of thermodynamics, indisputable in the macroscopic world, is challenged at the mesoscopic level: a mesoscopic isolated system, possessing spatial dimensions of the order of a few microns, is capable, as shown by a straightforward kinetic analysis, to exhibit a perpetuum mobile behavior associated with large negative variations of the Clausius entropy of the system. This violation of the Second Law is expedient for devising a cyclic process through which an isolated system can extract energy from a surrounding thermal bath.
The Stumbling Block of the Gibbs Entropy: the Reality of the Negative Absolute Temperatures
EPJ Web of Conferences, 2016
The second Tisza-Callen postulate of equilibrium thermodynamics states that for any system there exists a function of the system extensive parameters, called entropy, defined for all equilibrium states and having the property that the values assumed by the extensive parameters in the absence of a constraint are those that maximize the entropy over the manifold of constrained equilibrium states. Based on the thermodynamic evolution of systems which (in the Boltzmann description) have positive and negative temperatures, we show that this postulate is satisfied by the Boltzmann formula for the entropy and may be violated by the Gibbs formula, therefore invalidating the later. Vice versa, if we assume, by reductio ad absurdum, that for some thermodynamic systems the equilibrium state is determined by the Gibbs' prescription and not by Boltzmann's, this implies that such systems have macroscopic fluctuations and therefore do not reach the thermodynamic equilibrium.
Inconsistent thermostatistics and negative absolute temperatures
A considerable body of experimental and theoretical work claims the existence of negative absolute temperatures in spin systems and ultra-cold quantum gases. Here, we clarify that such findings can be attributed to the use of a popular yet inconsistent entropy definition, which violates fundamental thermodynamic relations and fails to produce sensible results for simple analytically tractable classical and quantum systems. Within a mathematically consistent thermodynamic formalism, based on an entropy concept originally derived by Gibbs, absolute temperature remains positive even for systems with bounded spectrum. We address spurious arguments against the Gibbs formalism and comment briefly on heat engines with efficiencies greater than one. arXiv:1304.2066v1 [cond-mat.stat-mech]
Positive and negative entropy production in thermodynamic systems
This article presents a heuristic combination of the local and global formulations of the second law of thermodynamics that suggests the possibility of theoretical existence of thermodynamic processes with positive and negative entropy production. Such processes may exhibit entropy couplings that reveal an unusual behavior from the point of view of conventional thermodynamics.
Positive and negative entropy production in thermodynamics systems
2008
This article presents a heuristic combination of the local and global formulations of the second law of thermodynamics that suggests the possibility of theoretical existence of thermodynamics processes with positive and negative entropy production.Such processes may exhibit entropy couplings that reveal an unusual behavior from the point of view of conventional thermodynamics.
The status of heat and work in nonequilibrium thermodynamics is quite confusing and nonunique at present with conflicting interpretations even after a long history of the first law dE(t) = d e Q(t) − dW e (t) in terms of exchange heat and work, and is far from settled. Moreover, the exchange quantities lack certain symmetry (see text). By generalizing the traditional concept to also include their time-dependent irreversible components d i Q(t) and d i W (t) allows us to express the first law in a symmetric form dE(t) = dQ(t) − dW (t) in which dQ(t) and work dW (t) appear on equal footing and possess the symmetry. We prove that d i Q(t) ≡ d i W (t); as a consequence, irreversible work turns into irreversible heat. Statistical analysis in terms of microstate probabilities p i (t) uniquely identifies dW (t) as isentropic and dQ(t) as isometric (see text) change in dE(t), a result known in equilibrium. We show that such a clear separation does not occur for d e Q(t) and dW e (t). Hence, our new formulation of the first law provides tremendous advantages and results in an extremely useful formulation of non-equilibrium thermodynamics, as we have shown recently [Phys. Rev. E 81, 051130 (2010); ibid 85, 041128 and 041129 (2012)]. We prove that an adiabatic process does not alter p i. All these results remain valid no matter how far the system is out of equilibrium. When the system is in internal equilibrium, dQ(t) ≡ T (t)dS(t) in terms of the instantaneous temperature T (t) of the system, which is reminiscent of equilibrium, even though, neither d e Q(t) ≡ T (t)d e S(t) nor d i Q(t) ≡ T (t)d i S(t). Indeed, d i Q(t) and d i S(t) have very different physics. We express these quantities in terms of d e p i (t) and d i p i (t), and demonstrate that p i (t) has a form very different from that in equilibrium. The first and second laws are no longer independent so that we need only one law, which is again reminiscent of equilibrium. The traditional formulas like the Clausius inequality d e Q(t)/T 0 < 0, ∆ e W < −∆ [E(t − T 0 S(t))], etc. become equalities dQ(t)/T (t) ≡ 0, ∆W = −∆ [E(t − T (t)S(t)], etc, a quite remarkable but unexpected result in view of the fact that ∆ i S(t) > 0. We identify the uncompensated transformation N (t, τ) during a cycle. We determine the irreversible components in two simple cases to show the usefulness of our approach; here, the traditional formulation is of no use. Our extension bring about a very strong parallel between equilibrium and non-equilibrium thermodynamics, except that one has irreversible entropy generation d i S(t) > 0 in the latter.
Negative temperatures and the definition of entropy
The concept of negative temperature has recently received renewed interest in the context of debates about the correct definition of the thermodynamic entropy in statistical mechanics. Faced with what they regard as a choice of entropy definitions from among a limited set of options, a number of researchers have identified the thermodynamic entropy with the "volume entropy" suggested by Gibbs, and further concluded that by this definition, negative temperatures violate the principles of thermodynamics. We regard none of the options considered for the entropy by these authors as adequate, and we disagree with their conclusions. We demonstrate that Gibbs' volume entropy is inconsistent with the postulates of thermodynamics for systems with inverted energy distributions, while a definition of entropy based on the probability distributions of observable macroscopic variables does satisfy the postulates of thermodynamics. Our results affirm that negative temperature is a valid concept in thermodynamics.
Physics of negative absolute temperatures
Physical Review E
Negative absolute temperatures were introduced into experimental physics by Purcell and Pound, who successfully applied this concept to nuclear spins; nevertheless the concept has proved controversial : a recent article aroused considerable interest by its claim, based on a classical entropy formula (the 'volume entropy') due to Gibbs, that negative temperatures violated basic principles of statistical thermodynamics. Here we give a thermodynamic analysis which confirms the negative-temperature interpretation of the Purcell-Pound experiments. We also examine the principal arguments that have been advanced against the negative temperature concept; we find that these arguments are not logically compelling and moreover that the underlying 'volume' entropy formula leads to predictions inconsistent with existing experimental results on nuclear spins. We conclude that, despite the counter-arguments, negative absolute temperatures make good theoretical sense and did occur in the experiments designed to produce them.